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Deck 3: Applications of Differentiation
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Question
Find the most general antiderivative of the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find f.
Question
A particle moves along a straight line with velocity function 
and its initial displacement is 
. Find its position function.
and its initial displacement is . Find its position function. Question
A company estimates that the marginal cost (in dollars per item) of producing items is 
. If the cost of producing one item is $560 find the cost of producing 400 items.
. If the cost of producing one item is $560 find the cost of producing 400 items. Question
Find the most general antiderivative of the function. 
Question
Find the most general antiderivative of the function. 
Question
A ballast is dropped from a stationary hot-air balloon that is at an altitude of 256 ft. Find (a) an expression for the altitude of the ballast after t seconds, (b) the time when it strikes the ground, and (c) its velocity when it strikes the ground. (Disregard air resistance and take 
.)
.) Question
Question
A car braked with a constant deceleration of 
, producing skid marks measuring 500 ft before coming to a stop. How fast was the car traveling when the brakes were first applied?
, producing skid marks measuring 500 ft before coming to a stop. How fast was the car traveling when the brakes were first applied? Question
Question
Given that the graph of f passes through the point (4, 69) and that the slope of its tangent line at 
is 
, find f (1) .
A)11
B)1
C)0
D)12
E)6
is , find f (1) .A)11
B)1
C)0
D)12
E)6
Question
Estimate the value of 
by using three iterations of Newton's method to solve the equation 
with initial estimate 
Round your final estimate to four decimal places.
A)1.71
B)2.2662
C)2.2361
D)1.6535
by using three iterations of Newton's method to solve the equation with initial estimate Round your final estimate to four decimal places.A)1.71
B)2.2662
C)2.2361
D)1.6535
Question
Suppose the line 
is tangent to the curve 
when 
. If Newton's method is used to locate a root of the equation 
and the initial approximation is 
, find the second approximation 
.
is tangent to the curve when . If Newton's method is used to locate a root of the equation and the initial approximation is , find the second approximation . Question
Evaluate 
, and tell whether its antiderivative F is increasing or decreasing at the point 
radians.
A)-0.288, increasing
B)0.757, increasing
C) -0.757, decreasing
D)0.277, decreasing
E)0.757, decreasing
, and tell whether its antiderivative F is increasing or decreasing at the point radians.A)-0.288, increasing
B)0.757, increasing
C) -0.757, decreasing
D)0.277, decreasing
E)0.757, decreasing
Question
Use Newton's method to approximate the zero of 
between 
and 
using 
. Continue until two successive approximations differ by less than 0.00001.
A)0.16904
B)0.11154
C)0.23624
D)0.07984
between and using . Continue until two successive approximations differ by less than 0.00001.A)0.16904
B)0.11154
C)0.23624
D)0.07984
Question
Use Newton's method to approximate the indicated root of 
in the interval 
, correct to six decimal places.
Use
as the initial approximation.
in the interval , correct to six decimal places.Use
as the initial approximation. Question
The size of the monthly repayment k that amortizes a loan of A dollars in N years at an interest rate of r per year, compounded monthly, on the unpaid balance is given by 
The value of r can be found by performing the iteration 
A family secured a loan of $360,000 from a bank to finance the purchase of a house. They have agreed to repay the loan in equal monthly installments of $2476 over 25 years. Find the interest rate on this loan. Round the rate to one decimal place.
A)8.7%
B)7.7%
C)6.7%
D)5.7%
The value of r can be found by performing the iteration A family secured a loan of $360,000 from a bank to finance the purchase of a house. They have agreed to repay the loan in equal monthly installments of $2476 over 25 years. Find the interest rate on this loan. Round the rate to one decimal place.A)8.7%
B)7.7%
C)6.7%
D)5.7%
Question
Find the position function of a particle moving along a coordinate line that satisfies the given condition. 
, s(1) = -1
, s(1) = -1 Question
Use Newton's method with the specified initial approximation 
to find 
, the third approximation to the root of the given equation. (Give your answer to four decimal places.) 
to find , the third approximation to the root of the given equation. (Give your answer to four decimal places.) Question
Find the position function of a particle moving along a coordinate line that satisfies the given conditions. 
, s(0) = 5, v(0) = 0
, s(0) = 5, v(0) = 0 Question
Use Newton's method to find the point of intersection of the graphs of 
and 
to within 0.00001 by solving the equation 
using 
and to within 0.00001 by solving the equation using Question
What is the shortest possible length of the line segment that is cut off by the first quadrant and is tangent to the curve 
at some point?
A)
B)
C)
D)
E)None of these
at some point?A)
B)
C)
D)
E)None of these
Question
A woman at a point A on the shore of a circular lake with radius 
wants to arrive at the point C diametrically opposite on the other side of the lake in the shortest possible time. She can walk at the rate of 
and row a boat at 
. How should she proceed? (Find 
). Round the result, if necessary, to the nearest hundredth. 
A)
radians
B)She should walk around the lake from point A to point C.
C)She should row from point A to point C radians
D)
radians
E)
radians
wants to arrive at the point C diametrically opposite on the other side of the lake in the shortest possible time. She can walk at the rate of and row a boat at . How should she proceed? (Find ). Round the result, if necessary, to the nearest hundredth. A)
radiansB)She should walk around the lake from point A to point C.
C)She should row from point A to point C radians
D)
radiansE)
radians Question
Find the smallest possible area of an isosceles triangle that is circumscribed about a circle of radius 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
The sum of two positive numbers is 
. What is the smallest possible value of the sum of their squares?
. What is the smallest possible value of the sum of their squares? Question
Find two positive numbers whose product is 
and whose sum is a minimum.
A)2, 72
B)3, 48
C)6, 24
D)
E)
and whose sum is a minimum.A)2, 72
B)3, 48
C)6, 24
D)
E)
Question
Consider the following problem: A farmer with 
ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens?
A)
B)
C)
D)
E)
ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens?A)
B)
C)
D)
E)
Question
A manufacturer has been selling 1,200 television sets a week at $400 each. A market survey indicates that for each $30 rebate offered to the buyer, the number of sets sold will increase by 60 per week. Find the demand function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
A rectangular beam will be cut from a cylindrical log of radius 
inches. Suppose that the strength of a rectangular beam is proportional to the product of its width and the square of its depth. Find the dimensions of the strongest beam that can be cut from the cylindrical log. 
A)
in, 
in
B)
in, 
in
C)
in, 
in
D)
in, 
in
E)
in, 
in
inches. Suppose that the strength of a rectangular beam is proportional to the product of its width and the square of its depth. Find the dimensions of the strongest beam that can be cut from the cylindrical log. A)
in, inB)
in, inC)
in, inD)
in, inE)
in, in Question
A production editor decided that a promotional flyer should have a 1-in. margin at the top and the bottom, and a 
-in. margin on each side. The editor further stipulated that the flyer should have an area of 288 
. Determine the dimensions of the flyer that will result in the maximum printed area on the flyer. 
A)
in. 
in.
B)
in. 
in.
C)12 in.
24 in.
D)6 in.
48 in.
-in. margin on each side. The editor further stipulated that the flyer should have an area of 288 . Determine the dimensions of the flyer that will result in the maximum printed area on the flyer. A)
in. in.B)
in. in.C)12 in.
24 in.D)6 in.
48 in. Question
Use Newton's method to approximate the zero of 
between 
and 
using 
. Continue until two successive approximations differ by less than 0.00001.
between and using . Continue until two successive approximations differ by less than 0.00001. Question
A piece of wire 
m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How should the wire be cut for the square so that the total area enclosed is a minimum? Round your answer to the nearest hundredth.
A)
B)
C)
D)
E)
m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How should the wire be cut for the square so that the total area enclosed is a minimum? Round your answer to the nearest hundredth.A)
B)
C)
D)
E)
Question
Approximate the zero of 
in 
to within 0.00001.
in to within 0.00001. Question
Use Newton's method to find the zero of 
to within 0.00001 by solving the equation 
using 
to within 0.00001 by solving the equation using Question
Approximate the zero of 
in 
to within 0.00001.
in to within 0.00001. Question
A right circular cylinder is inscribed in a sphere of radius 
. Find the largest possible surface area of such a cylinder. Round the result to the nearest hundredth.
A)
B)
C)
D)
E)
. Find the largest possible surface area of such a cylinder. Round the result to the nearest hundredth.A)
B)
C)
D)
E)
Question
The average cost of producing x units of a commodity is given by the equation 
.
Find the marginal cost at a production level of 1,255 units.
.Find the marginal cost at a production level of 1,255 units.
Question
Find the dimensions of the rectangle enclosed in the semicircle 
with the largest possible area. 
A)
in. 
in.
B)5 in.
7 in.
C)
in. 
in.
D)
in. 
in.
with the largest possible area. A)
in. in.B)5 in.
7 in.C)
in. in.D)
in. in. Question
Find the dimensions of a rectangle of area 400 
that has the smallest possible perimeter.
A)4 ft by 100 ft
B)1 ft by 400 ft
C)20 ft by 20 ft
D)2 ft by 200 ft
that has the smallest possible perimeter.A)4 ft by 100 ft
B)1 ft by 400 ft
C)20 ft by 20 ft
D)2 ft by 200 ft
Question
Find the point on the line 
that is closest to the origin.
A)
B)
C)
D)
E)
that is closest to the origin.A)
B)
C)
D)
E)
Question
An aircraft manufacturer wants to determine the best selling price for a new airplane. The company estimates that the initial cost of designing the airplane and setting up the factories in which to build it will be 
million dollars. The additional cost of manufacturing each plane can be modeled by the function 
where x is the number of aircraft produced and m is the manufacturing cost, in millions of dollars. The company estimates that if it charges a price p (in millions of dollars) for each plane, it will be able to sell 
.
Find the cost function.
million dollars. The additional cost of manufacturing each plane can be modeled by the function where x is the number of aircraft produced and m is the manufacturing cost, in millions of dollars. The company estimates that if it charges a price p (in millions of dollars) for each plane, it will be able to sell .Find the cost function.
Question
The manager of a 
-unit apartment complex knows from experience that all units will be occupied if the rent is 
per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 
increase in rent. What rent should the manager charge to maximize revenue?
-unit apartment complex knows from experience that all units will be occupied if the rent is per month. A market survey suggests that, on the average, one additional unit will remain vacant for each increase in rent. What rent should the manager charge to maximize revenue? Question
If 
of material is available to make a box with a square base and an open top, find the largest possible volume of the box.
of material is available to make a box with a square base and an open top, find the largest possible volume of the box. Question
For what values of 
does the curve have maximum and minimum points for the given function 
?
A)
B)
C)
D)
E)
does the curve have maximum and minimum points for the given function ?A)
B)
C)
D)
E)
Question
Find an equation of the line through the point 
that cuts off the least area from the first quadrant.
that cuts off the least area from the first quadrant. Question
Find the maximum area of a rectangle that can be circumscribed about a given rectangle with length 
and width 
. 
and width . Question
What is the function of the graph? 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
A woman is on a lake in a rowboat located one mile form the closest point P of a straight shoreline (see the figure). She wishes to get to point Q, 8 miles along the shore from P, by rowing to a point R between P and Q and then walking the rest of the distance. If she can row at a speed of 3 mph and walk at a speed of 4 mph, how should she pick the point R to get to Q as quickly as possible? How much time does she require?
8 mi 
8 mi Question
The owner of a ranch has 4000 yd of fencing with which to enclose a rectangular piece of grazing land situated along a straight portion of a river. If fencing is not required along the river, what are the dimensions of the largest area he can enclose? What is the area? 
Question
Question
For what values of 
does the curve have maximum and minimum points for the given function 
? Select the correct answer.
A)For
a parabola whose vertex 
, is the absolute maximum.For 
opens downward with one minimum points.For 
the graph opens upward, and has an absolute maximum at 
and no local minimum.
B)For
a parabola whose vertex 
, is the absolute maximum.For 
opens downward with two maximum points.For 
the graph opens upward, and has an absolute minimum at 
.
C)For
a parabola whose vertex 
, is the absolute maximum.For 
opens upward with two minimum points.For 
the graph opens downward, and has an absolute minimum at 
and no local minimum.
D)For
a parabola whose vertex 
, is the absolute maximum.For 
opens upward with two minimum points.For 
the graph opens downward, and has an absolute maximum at 
and no local minimum.
E)For
a parabola whose vertex 
, is the absolute maximum.For 
opens upward with two minimum points.For 
the graph opens downward, and has an absolute minimum at 
and no local minimum.
does the curve have maximum and minimum points for the given function ? Select the correct answer.A)For
a parabola whose vertex , is the absolute maximum.For opens downward with one minimum points.For the graph opens upward, and has an absolute maximum at and no local minimum.B)For
a parabola whose vertex , is the absolute maximum.For opens downward with two maximum points.For the graph opens upward, and has an absolute minimum at .C)For
a parabola whose vertex , is the absolute maximum.For opens upward with two minimum points.For the graph opens downward, and has an absolute minimum at and no local minimum.D)For
a parabola whose vertex , is the absolute maximum.For opens upward with two minimum points.For the graph opens downward, and has an absolute maximum at and no local minimum.E)For
a parabola whose vertex , is the absolute maximum.For opens upward with two minimum points.For the graph opens downward, and has an absolute minimum at and no local minimum. Question
Select the correct graph for the given function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the semicircle is equal to the width of the rectangle.) If the perimeter of the window is 
ft, find the dimensions of the window so that the greatest possible amount of light is admitted.
ft, find the dimensions of the window so that the greatest possible amount of light is admitted. Question
Find the point on the line 
that is closest to the origin.
that is closest to the origin. Question
Question
What is the function of the graph? 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
A steel pipe is being carried down a hallway 14 ft wide. At the end of the hall there is a right-angled turn into a narrower hallway 6 ft wide. What is the length of the longest pipe that can be carried horizontally around the corner? 
Question
A fence 
ft tall runs parallel to a tall building at a distance of 
ft from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building? Round the result to the nearest hundredth.
ft tall runs parallel to a tall building at a distance of ft from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building? Round the result to the nearest hundredth. Question
Question
Question
Sketch the graph of the function 
using the curve-sketching guidelines.
using the curve-sketching guidelines. Question
Sketch the curve. 
A)
B)
C)
A)
B)
C)
Question
Sketch the curve. Find the equation of the slant asymptote. 
Question
An efficiency study showed that the total number of cell phones assembled by the average worker at a manufacturing company t hours after starting work at 8 a.m.is given by 
Sketch the graph of the function N, and interpret your result.
Sketch the graph of the function N, and interpret your result.
Question
Sketch the graph of the function 
using the curve-sketching guidelines.
A)
B)
C)
D)
using the curve-sketching guidelines.A)
B)
C)
D)
Question
Find the horizontal and vertical asymptotes of the graph of the function 
.
A)HA
, VA 
B)HA
, VA none
C)HA
, VA none
D)HA
, VA 
.A)HA
, VA B)HA
, VA noneC)HA
, VA noneD)HA
, VA Question
Find the slant asymptote of the graph of 
using the curve-sketching guidelines.
A)
B)
C)
D)
using the curve-sketching guidelines.A)
B)
C)
D)
Question
A skydiver leaps from a helicopter hovering high above the ground. Her velocity t sec later and before deploying her parachute is given by 
where 
is measured in meters per second. What is her terminal velocity? Hint: Evaluate 
A)
m/sec
B)
m/sec
C)
m/sec
D)
m/sec
where is measured in meters per second. What is her terminal velocity? Hint: Evaluate A)
m/secB)
m/secC)
m/secD)
m/sec Question
Find the limit. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the limit. 
A)
B)0
C)
D)
A)
B)0
C)
D)
Question
Sketch the curve. 
A)
B)
C)
A)
B)
C)
Question
Sketch the graph of the function 
using the curve-sketching guidelines.
A)
B)
C)
D)
using the curve-sketching guidelines.A)
B)
C)
D)
Question
Sketch the graph of the function 
using the curve-sketching guidelines.
A)
B)
C)
D)
using the curve-sketching guidelines.A)
B)
C)
D)
Question
Sketch the graph of the function 
using the curve-sketching guidelines.
using the curve-sketching guidelines. Question
Sketch the graph of the function 
using the curve-sketching guidelines.
A)
B)
C)
D)
using the curve-sketching guidelines.A)
B)
C)
D)
Question
Sketch the graph of the function 
on 
using the curve-sketching guidelines.
on using the curve-sketching guidelines. Question
Sketch the graph of the function 
using the curve-sketching guidelines.
using the curve-sketching guidelines. Question
Sketch the curve. 
, 
A)
B)
C)
, A)
B)
C)
Question
Let 
and 
be polynomials. Find 
if the degree of 
is 
and the degree of 
is 
.
A)
B)
C)
D)
E)
and be polynomials. Find if the degree of is and the degree of is .A)
B)
C)
D)
E)
Question
Find the slant asymptote of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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Deck 3: Applications of Differentiation
1
Find the most general antiderivative of the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
2
Find f.
3
A particle moves along a straight line with velocity function and its initial displacement is . Find its position function.
and its initial displacement is . Find its position function.
4
A company estimates that the marginal cost (in dollars per item) of producing items is . If the cost of producing one item is $560 find the cost of producing 400 items.
. If the cost of producing one item is $560 find the cost of producing 400 items. Unlock Deck
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5
Find the most general antiderivative of the function.
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6
Find the most general antiderivative of the function.
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7
A ballast is dropped from a stationary hot-air balloon that is at an altitude of 256 ft. Find (a) an expression for the altitude of the ballast after t seconds, (b) the time when it strikes the ground, and (c) its velocity when it strikes the ground. (Disregard air resistance and take .)
.) Unlock Deck
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8
What constant acceleration is required to increase the speed of a car from 30 ft/s to 45 ft/s in
4 s?
4 s?
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9
A car braked with a constant deceleration of , producing skid marks measuring 500 ft before coming to a stop. How fast was the car traveling when the brakes were first applied?
, producing skid marks measuring 500 ft before coming to a stop. How fast was the car traveling when the brakes were first applied? Unlock Deck
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10
To what constant deceleration would a car moving along a straight road be subjected if the car were brought to rest from a speed of 86 ft/sec in 7 sec? What would the stopping distance be?
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11
Given that the graph of f passes through the point (4, 69) and that the slope of its tangent line at is , find f (1) .
A)11
B)1
C)0
D)12
E)6
is , find f (1) .A)11
B)1
C)0
D)12
E)6
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12
Estimate the value of by using three iterations of Newton's method to solve the equation with initial estimate Round your final estimate to four decimal places.
A)1.71
B)2.2662
C)2.2361
D)1.6535
by using three iterations of Newton's method to solve the equation with initial estimate Round your final estimate to four decimal places.A)1.71
B)2.2662
C)2.2361
D)1.6535
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13
Suppose the line is tangent to the curve when . If Newton's method is used to locate a root of the equation and the initial approximation is , find the second approximation .
is tangent to the curve when . If Newton's method is used to locate a root of the equation and the initial approximation is , find the second approximation . Unlock Deck
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14
Evaluate , and tell whether its antiderivative F is increasing or decreasing at the point radians.
A)-0.288, increasing
B)0.757, increasing
C) -0.757, decreasing
D)0.277, decreasing
E)0.757, decreasing
, and tell whether its antiderivative F is increasing or decreasing at the point radians.A)-0.288, increasing
B)0.757, increasing
C) -0.757, decreasing
D)0.277, decreasing
E)0.757, decreasing
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15
Use Newton's method to approximate the zero of between and using . Continue until two successive approximations differ by less than 0.00001.
A)0.16904
B)0.11154
C)0.23624
D)0.07984
between and using . Continue until two successive approximations differ by less than 0.00001.A)0.16904
B)0.11154
C)0.23624
D)0.07984
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16
Use Newton's method to approximate the indicated root of in the interval , correct to six decimal places.
Use as the initial approximation.
in the interval , correct to six decimal places.Use
as the initial approximation. Unlock Deck
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17
The size of the monthly repayment k that amortizes a loan of A dollars in N years at an interest rate of r per year, compounded monthly, on the unpaid balance is given by The value of r can be found by performing the iteration A family secured a loan of $360,000 from a bank to finance the purchase of a house. They have agreed to repay the loan in equal monthly installments of $2476 over 25 years. Find the interest rate on this loan. Round the rate to one decimal place.
A)8.7%
B)7.7%
C)6.7%
D)5.7%
The value of r can be found by performing the iteration A family secured a loan of $360,000 from a bank to finance the purchase of a house. They have agreed to repay the loan in equal monthly installments of $2476 over 25 years. Find the interest rate on this loan. Round the rate to one decimal place.A)8.7%
B)7.7%
C)6.7%
D)5.7%
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18
Find the position function of a particle moving along a coordinate line that satisfies the given condition. , s(1) = -1
, s(1) = -1 Unlock Deck
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19
Use Newton's method with the specified initial approximation to find , the third approximation to the root of the given equation. (Give your answer to four decimal places.)
to find , the third approximation to the root of the given equation. (Give your answer to four decimal places.) Unlock Deck
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20
Find the position function of a particle moving along a coordinate line that satisfies the given conditions. , s(0) = 5, v(0) = 0
, s(0) = 5, v(0) = 0 Unlock Deck
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21
Use Newton's method to find the point of intersection of the graphs of and to within 0.00001 by solving the equation using
and to within 0.00001 by solving the equation using Unlock Deck
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22
What is the shortest possible length of the line segment that is cut off by the first quadrant and is tangent to the curve at some point?
A)
B)
C)
D)
E)None of these
at some point?A)
B)
C)
D)
E)None of these
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23
A woman at a point A on the shore of a circular lake with radius wants to arrive at the point C diametrically opposite on the other side of the lake in the shortest possible time. She can walk at the rate of and row a boat at . How should she proceed? (Find ). Round the result, if necessary, to the nearest hundredth.
A) radians
B)She should walk around the lake from point A to point C.
C)She should row from point A to point C radians
D) radians
E) radians
wants to arrive at the point C diametrically opposite on the other side of the lake in the shortest possible time. She can walk at the rate of and row a boat at . How should she proceed? (Find ). Round the result, if necessary, to the nearest hundredth. A)
radiansB)She should walk around the lake from point A to point C.
C)She should row from point A to point C radians
D)
radiansE)
radians Unlock Deck
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24
Find the smallest possible area of an isosceles triangle that is circumscribed about a circle of radius .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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25
The sum of two positive numbers is . What is the smallest possible value of the sum of their squares?
. What is the smallest possible value of the sum of their squares? Unlock Deck
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26
Find two positive numbers whose product is and whose sum is a minimum.
A)2, 72
B)3, 48
C)6, 24
D)
E)
and whose sum is a minimum.A)2, 72
B)3, 48
C)6, 24
D)
E)
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27
Consider the following problem: A farmer with ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens?
A)
B)
C)
D)
E)
ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens?A)
B)
C)
D)
E)
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28
A manufacturer has been selling 1,200 television sets a week at $400 each. A market survey indicates that for each $30 rebate offered to the buyer, the number of sets sold will increase by 60 per week. Find the demand function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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29
A rectangular beam will be cut from a cylindrical log of radius inches. Suppose that the strength of a rectangular beam is proportional to the product of its width and the square of its depth. Find the dimensions of the strongest beam that can be cut from the cylindrical log.
A) in, in
B) in, in
C) in, in
D) in, in
E) in, in
inches. Suppose that the strength of a rectangular beam is proportional to the product of its width and the square of its depth. Find the dimensions of the strongest beam that can be cut from the cylindrical log. A)
in, inB)
in, inC)
in, inD)
in, inE)
in, in Unlock Deck
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30
A production editor decided that a promotional flyer should have a 1-in. margin at the top and the bottom, and a -in. margin on each side. The editor further stipulated that the flyer should have an area of 288 . Determine the dimensions of the flyer that will result in the maximum printed area on the flyer.
A) in. in.
B) in. in.
C)12 in. 24 in.
D)6 in. 48 in.
-in. margin on each side. The editor further stipulated that the flyer should have an area of 288 . Determine the dimensions of the flyer that will result in the maximum printed area on the flyer. A)
in. in.B)
in. in.C)12 in.
24 in.D)6 in.
48 in. Unlock Deck
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31
Use Newton's method to approximate the zero of between and using . Continue until two successive approximations differ by less than 0.00001.
between and using . Continue until two successive approximations differ by less than 0.00001. Unlock Deck
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32
A piece of wire m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How should the wire be cut for the square so that the total area enclosed is a minimum? Round your answer to the nearest hundredth.
A)
B)
C)
D)
E)
m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How should the wire be cut for the square so that the total area enclosed is a minimum? Round your answer to the nearest hundredth.A)
B)
C)
D)
E)
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33
Approximate the zero of in to within 0.00001.
in to within 0.00001. Unlock Deck
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34
Use Newton's method to find the zero of to within 0.00001 by solving the equation using
to within 0.00001 by solving the equation using Unlock Deck
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35
Approximate the zero of in to within 0.00001.
in to within 0.00001. Unlock Deck
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36
A right circular cylinder is inscribed in a sphere of radius . Find the largest possible surface area of such a cylinder. Round the result to the nearest hundredth.
A)
B)
C)
D)
E)
. Find the largest possible surface area of such a cylinder. Round the result to the nearest hundredth.A)
B)
C)
D)
E)
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37
The average cost of producing x units of a commodity is given by the equation .
Find the marginal cost at a production level of 1,255 units.
.Find the marginal cost at a production level of 1,255 units.
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38
Find the dimensions of the rectangle enclosed in the semicircle with the largest possible area.
A) in. in.
B)5 in. 7 in.
C) in. in.
D) in. in.
with the largest possible area. A)
in. in.B)5 in.
7 in.C)
in. in.D)
in. in. Unlock Deck
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39
Find the dimensions of a rectangle of area 400 that has the smallest possible perimeter.
A)4 ft by 100 ft
B)1 ft by 400 ft
C)20 ft by 20 ft
D)2 ft by 200 ft
that has the smallest possible perimeter.A)4 ft by 100 ft
B)1 ft by 400 ft
C)20 ft by 20 ft
D)2 ft by 200 ft
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40
Find the point on the line that is closest to the origin.
A)
B)
C)
D)
E)
that is closest to the origin.A)
B)
C)
D)
E)
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41
An aircraft manufacturer wants to determine the best selling price for a new airplane. The company estimates that the initial cost of designing the airplane and setting up the factories in which to build it will be million dollars. The additional cost of manufacturing each plane can be modeled by the function where x is the number of aircraft produced and m is the manufacturing cost, in millions of dollars. The company estimates that if it charges a price p (in millions of dollars) for each plane, it will be able to sell .
Find the cost function.
million dollars. The additional cost of manufacturing each plane can be modeled by the function where x is the number of aircraft produced and m is the manufacturing cost, in millions of dollars. The company estimates that if it charges a price p (in millions of dollars) for each plane, it will be able to sell .Find the cost function.
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42
The manager of a -unit apartment complex knows from experience that all units will be occupied if the rent is per month. A market survey suggests that, on the average, one additional unit will remain vacant for each increase in rent. What rent should the manager charge to maximize revenue?
-unit apartment complex knows from experience that all units will be occupied if the rent is per month. A market survey suggests that, on the average, one additional unit will remain vacant for each increase in rent. What rent should the manager charge to maximize revenue? Unlock Deck
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43
If of material is available to make a box with a square base and an open top, find the largest possible volume of the box.
of material is available to make a box with a square base and an open top, find the largest possible volume of the box. Unlock Deck
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44
For what values of does the curve have maximum and minimum points for the given function ?
A)
B)
C)
D)
E)
does the curve have maximum and minimum points for the given function ?A)
B)
C)
D)
E)
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45
Find an equation of the line through the point that cuts off the least area from the first quadrant.
that cuts off the least area from the first quadrant. Unlock Deck
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46
Find the maximum area of a rectangle that can be circumscribed about a given rectangle with length and width .
and width . Unlock Deck
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47
What is the function of the graph?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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48
A woman is on a lake in a rowboat located one mile form the closest point P of a straight shoreline (see the figure). She wishes to get to point Q, 8 miles along the shore from P, by rowing to a point R between P and Q and then walking the rest of the distance. If she can row at a speed of 3 mph and walk at a speed of 4 mph, how should she pick the point R to get to Q as quickly as possible? How much time does she require?
8 mi
8 mi Unlock Deck
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49
The owner of a ranch has 4000 yd of fencing with which to enclose a rectangular piece of grazing land situated along a straight portion of a river. If fencing is not required along the river, what are the dimensions of the largest area he can enclose? What is the area?
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50
A baseball team plays in a stadium that holds 56,000 spectators. With ticket prices at $9, the average attendance had been 32,000. When ticket prices were lowered to $8, the average attendance rose to 36,000. How should ticket prices be set to maximize revenue? Assume the demand function is linear.
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51
For what values of does the curve have maximum and minimum points for the given function ? Select the correct answer.
A)For a parabola whose vertex , is the absolute maximum.For opens downward with one minimum points.For the graph opens upward, and has an absolute maximum at and no local minimum.
B)For a parabola whose vertex , is the absolute maximum.For opens downward with two maximum points.For the graph opens upward, and has an absolute minimum at .
C)For a parabola whose vertex , is the absolute maximum.For opens upward with two minimum points.For the graph opens downward, and has an absolute minimum at and no local minimum.
D)For a parabola whose vertex , is the absolute maximum.For opens upward with two minimum points.For the graph opens downward, and has an absolute maximum at and no local minimum.
E)For a parabola whose vertex , is the absolute maximum.For opens upward with two minimum points.For the graph opens downward, and has an absolute minimum at and no local minimum.
does the curve have maximum and minimum points for the given function ? Select the correct answer.A)For
a parabola whose vertex , is the absolute maximum.For opens downward with one minimum points.For the graph opens upward, and has an absolute maximum at and no local minimum.B)For
a parabola whose vertex , is the absolute maximum.For opens downward with two maximum points.For the graph opens upward, and has an absolute minimum at .C)For
a parabola whose vertex , is the absolute maximum.For opens upward with two minimum points.For the graph opens downward, and has an absolute minimum at and no local minimum.D)For
a parabola whose vertex , is the absolute maximum.For opens upward with two minimum points.For the graph opens downward, and has an absolute maximum at and no local minimum.E)For
a parabola whose vertex , is the absolute maximum.For opens upward with two minimum points.For the graph opens downward, and has an absolute minimum at and no local minimum. Unlock Deck
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52
Select the correct graph for the given function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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53
A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the semicircle is equal to the width of the rectangle.) If the perimeter of the window is ft, find the dimensions of the window so that the greatest possible amount of light is admitted.
ft, find the dimensions of the window so that the greatest possible amount of light is admitted. Unlock Deck
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54
Find the point on the line that is closest to the origin.
that is closest to the origin. Unlock Deck
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55
A rectangular box having a top and a square base is to be constructed at a cost of $1. If the material for the bottom costs $0.35 per square foot, the material for the top costs $0.15 per square foot, and the material for the sides costs $0.20 per square foot, find the dimensions and volume of the box of maximum volume that can be constructed.
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56
What is the function of the graph?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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57
A steel pipe is being carried down a hallway 14 ft wide. At the end of the hall there is a right-angled turn into a narrower hallway 6 ft wide. What is the length of the longest pipe that can be carried horizontally around the corner?
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58
A fence ft tall runs parallel to a tall building at a distance of ft from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building? Round the result to the nearest hundredth.
ft tall runs parallel to a tall building at a distance of ft from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building? Round the result to the nearest hundredth. Unlock Deck
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59
Find two numbers whose difference is 170 and whose product is a minimum.
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60
If an open box is made from a metal sheet 9 in. square by cutting out identical squares from each corner an bending up the resulting flaps, determine the dimensions of the box with the largest volume that can be made.
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61
Sketch the graph of the function using the curve-sketching guidelines.
using the curve-sketching guidelines. Unlock Deck
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62
Sketch the curve.
A)
B)
C)
A)
B)
C)
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63
Sketch the curve. Find the equation of the slant asymptote.
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64
An efficiency study showed that the total number of cell phones assembled by the average worker at a manufacturing company t hours after starting work at 8 a.m.is given by
Sketch the graph of the function N, and interpret your result.
Sketch the graph of the function N, and interpret your result.
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65
Sketch the graph of the function using the curve-sketching guidelines.
A)
B)
C)
D)
using the curve-sketching guidelines.A)
B)
C)
D)
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66
Find the horizontal and vertical asymptotes of the graph of the function .
A)HA , VA
B)HA , VA none
C)HA , VA none
D)HA , VA
.A)HA
, VA B)HA
, VA noneC)HA
, VA noneD)HA
, VA Unlock Deck
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67
Find the slant asymptote of the graph of using the curve-sketching guidelines.
A)
B)
C)
D)
using the curve-sketching guidelines.A)
B)
C)
D)
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68
A skydiver leaps from a helicopter hovering high above the ground. Her velocity t sec later and before deploying her parachute is given by where is measured in meters per second. What is her terminal velocity? Hint: Evaluate
A) m/sec
B) m/sec
C) m/sec
D) m/sec
where is measured in meters per second. What is her terminal velocity? Hint: Evaluate A)
m/secB)
m/secC)
m/secD)
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69
Find the limit.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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70
Find the limit.
A)
B)0
C)
D)
A)
B)0
C)
D)
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71
Sketch the curve.
A)
B)
C)
A)
B)
C)
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72
Sketch the graph of the function using the curve-sketching guidelines.
A)
B)
C)
D)
using the curve-sketching guidelines.A)
B)
C)
D)
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73
Sketch the graph of the function using the curve-sketching guidelines.
A)
B)
C)
D)
using the curve-sketching guidelines.A)
B)
C)
D)
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74
Sketch the graph of the function using the curve-sketching guidelines.
using the curve-sketching guidelines. Unlock Deck
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75
Sketch the graph of the function using the curve-sketching guidelines.
A)
B)
C)
D)
using the curve-sketching guidelines.A)
B)
C)
D)
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76
Sketch the graph of the function on using the curve-sketching guidelines.
on using the curve-sketching guidelines. Unlock Deck
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77
Sketch the graph of the function using the curve-sketching guidelines.
using the curve-sketching guidelines. Unlock Deck
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78
Sketch the curve. ,
A)
B)
C)
, A)
B)
C)
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79
Let and be polynomials. Find if the degree of is and the degree of is .
A)
B)
C)
D)
E)
and be polynomials. Find if the degree of is and the degree of is .A)
B)
C)
D)
E)
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80
Find the slant asymptote of the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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