Question 1

Given f(x) = 3x3 -3x2 -8x + 7, find the intervals where f is concave up and where f is concave down.

Accepted Answer

Concave up

Question 2

Answer true or false. tan(3x + 8) has a point of inflection on   .

Accepted Answer

A) True 
 B)False

Question 3

An object moves a distance s away from the origin according to the equation s(t) = 7t3 - 2t + 3, where 0 $\le$ t $\le$ 12. At what time is the object farthest from the origin?

Accepted Answer

A)  0 
B)  12 
C)  3 
D)    
E)    
A)  0 
B)  12 
C)  3 
D)    
E)

Question 4

Suppose that the number of bacteria present in a culture bacteria at time t is given by N = -5000(t2 + 4t - 32). Find the smallest number of bacteria in the culture during the time interval 0 $\le$  t $\le$ 3.

Accepted Answer

A)  10,000 
B)  160,000 
C)  180,000 
D)  55,000 
E)  170,000 
A)  10,000 
B)  160,000 
C)  180,000 
D)  55,000 
E)  170,000

Question 5

An open-top shipping crate with square bottom and rectangular sides is to hold 108 in3 and requires a minimum amount of cardboard. Find the most economical dimensions.

Accepted Answer

Let x and y be the dimensions shown in t

Question 6

Let s(t) = 3t6. Find t when a = 0.

Accepted Answer

A)  6 
B)  90 
C)  0 
D)  18 
E)  2 
A)  6 
B)  90 
C)  0 
D)  18 
E)  2

Question 7

Find the area of the largest possible isosceles triangle with 2 sides equal to 12.

Accepted Answer

@#IMG-DLM& @#IMG-DLM& A = 72 s

Question 8

f(x) = 9x4 - 2x5 , find the location of any inflection points.

Accepted Answer

The answer of f(x) = 9x4 - 2x5 , find...

Question 9

Answer true or false. The hypotheses of the Mean-Value Theorem are satisfied for f(x) = cos 3x on [0, 4 $\pi$].

Accepted Answer

A) True 
 B)False

Question 10

Sketch the graph of y = x3 - 48x + 3. Find any stationary points and any points of inflection.

Accepted Answer

y' = 3x² -48 y'' =

Question 11

s(t) = 5t5- 11. Find t when a = 0.

Accepted Answer

A)  100 
B)  -100 
C)  5 
D)  -5 
E)  0 
A)  100 
B)  -100 
C)  5 
D)  -5 
E)  0

Question 12

If three sides of a trapezoid are a = 6 inches long, how long should the fourth side be if the area is a maximum? [Area of a trapezoid =   where a and b are the lengths of the parallel sides and h = height.]

Accepted Answer

Let x be as shown in the figur

Question 13

A cyclist starts from rest and travels 6.25 miles along a straight road in 15 minutes. Use the Mean-Value Theorem to show that at some instant during the trip his velocity was exactly 25 miles per hour.

Accepted Answer

Let s = f(t) be the position versus time

Question 14

A right triangle has a perimeter of 38. What are the lengths of each side if the area contained within the triangle is to be maximized?

Accepted Answer

A)    ,
  ,
  
B)  15, 15, 8 
C)    ,
  ,
  
D)    ,
  ,
  
E)  17, 17, 4 
A)    ,
  ,
  
B)  15, 15, 8 
C)    ,
  ,
  
D)    ,
  ,
  
E)  17, 17, 4

Question 15

Find the dimensions of the rectangle of greatest area that can be inscribed in a circle of radius a.

Accepted Answer

A = xy and x² + y²

Question 16

Use a graphing utility to estimate the absolute maximum of   on [2, 10].

Accepted Answer

The answer of Use a graphing utility to estimate the...

Question 17

Sketch the graph of   . Identify the vertical and horizontal asymptotes.

Accepted Answer

Vertical asymptote a

Question 18

Answer true or false. The hypotheses of the Mean-Value Theorem are satisfied for   on [-2, 2].

Accepted Answer

A) True 
 B)False

Question 19

If f(x) = x5- 2x + 4. Find the points of inflection.

Accepted Answer

The answer of If f(x) = x5- 2x + 4....

Question 20

Find the relative extrema for   .

Accepted Answer

Relative m

Given f(x) = 3x³ -3x² -8x + 7, find the intervals where f is concave up and where f is concave down.

Answer true or false. tan(3x + 8) has a point of inflection on .

An object moves a distance s away from the origin according to the equation s(t) = 7t³ - 2t + 3, where 0 $\le$ t $\le$ 12. At what time is the object farthest from the origin?

Suppose that the number of bacteria present in a culture bacteria at time t is given by N = -5000(t² + 4t - 32). Find the smallest number of bacteria in the culture during the time interval 0 $\le$ t $\le$ 3.

An open-top shipping crate with square bottom and rectangular sides is to hold 108 in³ and requires a minimum amount of cardboard. Find the most economical dimensions.

Let s(t) = 3t⁶. Find t when a = 0.

Find the area of the largest possible isosceles triangle with 2 sides equal to 12.

f(x) = 9x⁴ - 2x⁵ , find the location of any inflection points.

Answer true or false. The hypotheses of the Mean-Value Theorem are satisfied for f(x) = cos 3x on [0, 4 $\pi$ ].

Sketch the graph of y = x³ - 48x + 3. Find any stationary points and any points of inflection.

s(t) = 5t⁵- 11. Find t when a = 0.

If three sides of a trapezoid are a = 6 inches long, how long should the fourth side be if the area is a maximum? [Area of a trapezoid = where a and b are the lengths of the parallel sides and h = height.]

A cyclist starts from rest and travels 6.25 miles along a straight road in 15 minutes. Use the Mean-Value Theorem to show that at some instant during the trip his velocity was exactly 25 miles per hour.

A right triangle has a perimeter of 38. What are the lengths of each side if the area contained within the triangle is to be maximized?

Find the dimensions of the rectangle of greatest area that can be inscribed in a circle of radius a.

Use a graphing utility to estimate the absolute maximum of on [2, 10].

Sketch the graph of . Identify the vertical and horizontal asymptotes.

Answer true or false. The hypotheses of the Mean-Value Theorem are satisfied for on [-2, 2].

If f(x) = x⁵- 2x + 4. Find the points of inflection.

Find the relative extrema for .

Limits and Continuity

The Derivative

Topics in Deifferentiation

Integration

Applications of the Definite Integral in Geometry, Science and Engineering

Principle of Integral Evaluation

Mathematical Modeling With Differential Equations

Infinte Series

Parametric and Polar Curves; Conic Sections

Three-Dimensional Space; Vectors

Vector-Valued Functions

Partial Derivatives

Multiple Integrals

Topics in Vector Calculus

Filters

Exam 4: The Derivative in Graphing and Applications

Given f(x) = 3x3 -3x2 -8x + 7, find the intervals where f is concave up and where f is concave down.

Answer true or false. tan(3x + 8) has a point of inflection on .

An object moves a distance s away from the origin according to the equation s(t) = 7t3 - 2t + 3, where 0 ≤\le≤ t ≤\le≤ 12. At what time is the object farthest from the origin?

Suppose that the number of bacteria present in a culture bacteria at time t is given by N = -5000(t2 + 4t - 32). Find the smallest number of bacteria in the culture during the time interval 0 ≤\le≤ t ≤\le≤ 3.

An open-top shipping crate with square bottom and rectangular sides is to hold 108 in3 and requires a minimum amount of cardboard. Find the most economical dimensions.

Let s(t) = 3t6. Find t when a = 0.

Find the area of the largest possible isosceles triangle with 2 sides equal to 12.

f(x) = 9x4 - 2x5 , find the location of any inflection points.

Answer true or false. The hypotheses of the Mean-Value Theorem are satisfied for f(x) = cos 3x on [0, 4 π\piπ ].

Sketch the graph of y = x3 - 48x + 3. Find any stationary points and any points of inflection.

s(t) = 5t5- 11. Find t when a = 0.

If three sides of a trapezoid are a = 6 inches long, how long should the fourth side be if the area is a maximum? [Area of a trapezoid = where a and b are the lengths of the parallel sides and h = height.]

A cyclist starts from rest and travels 6.25 miles along a straight road in 15 minutes. Use the Mean-Value Theorem to show that at some instant during the trip his velocity was exactly 25 miles per hour.

A right triangle has a perimeter of 38. What are the lengths of each side if the area contained within the triangle is to be maximized?

Find the dimensions of the rectangle of greatest area that can be inscribed in a circle of radius a.

Use a graphing utility to estimate the absolute maximum of on [2, 10].

Sketch the graph of . Identify the vertical and horizontal asymptotes.

Answer true or false. The hypotheses of the Mean-Value Theorem are satisfied for on [-2, 2].

If f(x) = x5- 2x + 4. Find the points of inflection.

Find the relative extrema for .

Limits and Continuity

The Derivative

Topics in Deifferentiation

Integration

Applications of the Definite Integral in Geometry, Science and Engineering

Principle of Integral Evaluation

Mathematical Modeling With Differential Equations

Infinte Series

Parametric and Polar Curves; Conic Sections

Three-Dimensional Space; Vectors

Vector-Valued Functions

Partial Derivatives

Multiple Integrals

Topics in Vector Calculus

Filters

Given f(x) = 3x³ -3x² -8x + 7, find the intervals where f is concave up and where f is concave down.

An object moves a distance s away from the origin according to the equation s(t) = 7t³ - 2t + 3, where 0 $\le$ t $\le$ 12. At what time is the object farthest from the origin?

Suppose that the number of bacteria present in a culture bacteria at time t is given by N = -5000(t² + 4t - 32). Find the smallest number of bacteria in the culture during the time interval 0 $\le$ t $\le$ 3.

An open-top shipping crate with square bottom and rectangular sides is to hold 108 in³ and requires a minimum amount of cardboard. Find the most economical dimensions.

Let s(t) = 3t⁶. Find t when a = 0.

f(x) = 9x⁴ - 2x⁵ , find the location of any inflection points.

Answer true or false. The hypotheses of the Mean-Value Theorem are satisfied for f(x) = cos 3x on [0, 4 $\pi$ ].

Sketch the graph of y = x³ - 48x + 3. Find any stationary points and any points of inflection.

s(t) = 5t⁵- 11. Find t when a = 0.

If f(x) = x⁵- 2x + 4. Find the points of inflection.