Question 1

Approximate   by applying Newton's Method to the equation x3 - 88 = 0. Use 4 for your initial value and calculate nine iterations.

Accepted Answer

f(x) = x³ - 88 f '(x) = 3x

Question 2

If f(x) = 9x4 - 6x3 + 1 , find the inflection points.

Accepted Answer

The answer of If f(x) = 9x4 - 6x3 +...

Question 3

The stiffness of a beam of rectangular cross section is proportional to the product xy3. Find the stiffest beam which can be cut from a log with diameter d = 14 inches. See figure on right.

Accepted Answer

S = kxy³ and from the figure, x

Question 4

A sheet of cardboard 30 in square is used to make an open box by cutting squares of equal size from the corners and folding up the sides. What size squares should be cut to obtain a box with largest possible volume?

Accepted Answer

Volume is

Question 5

Determine the x-coordinate of each stationary point of f(x) = 3x2 -24x.

Accepted Answer

A)  x = 4 
B)  x = 8 and x = 0 
C)  x = 4 and x = 0 
D)  x = -8 
E)  None exist 
A)  x = 4 
B)  x = 8 and x = 0 
C)  x = 4 and x = 0 
D)  x = -8 
E)  None exist

Question 6

The position function of a particle is given by s(t) = 4t - 3t2 + 4t3. Find the velocity function.

Accepted Answer

v(t) = s'(

Question 7

If f(x) = (x - 7)4 + 3 , find the location of any inflection points.

Accepted Answer

No inflect

Question 8

A line is drawn through the point P(5, 2) so that it intersects the y-axis at A(0,y) and the x-axis at B(x,0). Find the smallest triangle formed if x and y are positive.

Accepted Answer

@#IMG-DLM& . The slope of the line throu

Question 9

The largest interval over which f is increasing for f(x) = x9 - 5 is

Accepted Answer

A)  (-$\infty$, -5] 
B)  [5, $\infty$) 
C)  (-$\infty$, $\infty$) 
D)  [-5, $\infty$) 
E)  (-$\infty$, 5] 
A)  (-$\infty$, -5] 
B)  [5, $\infty$) 
C)  (-$\infty$, $\infty$) 
D)  [-5, $\infty$) 
E)  (-$\infty$, 5]

Question 10

Sketch the graph of y = 7x4 -7x3 + 2. Find any stationary points and any points of inflection.

Accepted Answer

y' = 28x³ - 21x

Question 11

Answer true or false. Using a graphing utility it can be shown that f(x) = x4 sin 4x has a relative maximum on 0 < x < 2 $\pi$.

Accepted Answer

A) True 
 B)False

Question 12

Answer true or false. A fence is to be used to enclose a rectangular plot of land. If there are 920 feet of fencing, it can be shown that a 230 ft by 230 ft square is the rectangle that can be enclosed with the greatest area. (A square is considered a rectangle.)

Accepted Answer

A) True 
 B)False

Question 13

If f(x) = sin 2x (0,  $\pi$), find the intervals where f is concave up and where f is concave down.

Accepted Answer

The answer of If f(x) = sin 2x (0, ...

Question 14

The position function of a particle is given by s(t) = 8t + cos t. Find the velocity function.

Accepted Answer

The answer of The position function of a particle is...

Question 15

Verify that f(x) = x3 - 5x + 3 satisfies the hypothesis of the Mean-Value Theorem over the interval [-2, 3] and find all values of C that satisfy the conclusion of the theorem.

Accepted Answer

f(-2) = 5
f(3) = 9
f

Question 16

If f(x) = 3x4 -90x2 , find the intervals where f is concave up and where f is concave down.

Accepted Answer

Concave up

Question 17

Answer true or false. f(x) = | cot2x| has no relative extrema on   .

Accepted Answer

A) True 
 B)False

Question 18

Given   . Find any stationary points and any points of inflection. Also find any vertical and horizontal asymptotes.

Accepted Answer

@#IMG-DLM& @#IMG-DLM& Relative maximum at @#IMG-DLM& Inflect

Question 19

Let s(t) = t4 - 5t + 6 be a position function. The acceleration function a(t) =

Accepted Answer

A)  4t3 - 5 
B)  12t2 
C)  4t3 - 5t 
D)  12t2 - 5 
E)  12t3 
A)  4t3 - 5 
B)  12t2 
C)  4t3 - 5t 
D)  12t2 - 5 
E)  12t3

Question 20

Answer true or false. If f ''(-8) = -10 and f ''(8) = 10, then there must be a point of inflection on (-8, 8).

Accepted Answer

A) True 
 B)False

Approximate by applying Newton's Method to the equation x³ - 88 = 0. Use 4 for your initial value and calculate nine iterations.

If f(x) = 9x⁴ - 6x³ + 1 , find the inflection points.

The stiffness of a beam of rectangular cross section is proportional to the product xy³. Find the stiffest beam which can be cut from a log with diameter d = 14 inches. See figure on right.

A sheet of cardboard 30 in square is used to make an open box by cutting squares of equal size from the corners and folding up the sides. What size squares should be cut to obtain a box with largest possible volume?

Determine the x-coordinate of each stationary point of f(x) = 3x² -24x.

The position function of a particle is given by s(t) = 4t - 3t² + 4t³. Find the velocity function.

If f(x) = (x - 7)⁴ + 3 , find the location of any inflection points.

A line is drawn through the point P(5, 2) so that it intersects the y-axis at A(0,y) and the x-axis at B(x,0). Find the smallest triangle formed if x and y are positive.

The largest interval over which f is increasing for f(x) = x⁹ - 5 is

Sketch the graph of y = 7x⁴ -7x³ + 2. Find any stationary points and any points of inflection.

Answer true or false. Using a graphing utility it can be shown that f(x) = x⁴ sin 4x has a relative maximum on 0 < x < 2 $\pi$ .

Answer true or false. A fence is to be used to enclose a rectangular plot of land. If there are 920 feet of fencing, it can be shown that a 230 ft by 230 ft square is the rectangle that can be enclosed with the greatest area. (A square is considered a rectangle.)

If f(x) = sin 2x (0, $\pi$ ), find the intervals where f is concave up and where f is concave down.

The position function of a particle is given by s(t) = 8t + cos t. Find the velocity function.

Verify that f(x) = x³ - 5x + 3 satisfies the hypothesis of the Mean-Value Theorem over the interval [-2, 3] and find all values of C that satisfy the conclusion of the theorem.

If f(x) = 3x⁴ -90x²_,find the intervals where f is concave up and where f is concave down.

Answer true or false. f(x) = | cot²x| has no relative extrema on .

Given . Find any stationary points and any points of inflection. Also find any vertical and horizontal asymptotes.

Let s(t) = t⁴ - 5t + 6 be a position function. The acceleration function a(t) =

Answer true or false. If f ''(-8) = -10 and f ''(8) = 10, then there must be a point of inflection on (-8, 8).

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

Approximate by applying Newton's Method to the equation x3 - 88 = 0. Use 4 for your initial value and calculate nine iterations.

If f(x) = 9x4 - 6x3 + 1 , find the inflection points.

The stiffness of a beam of rectangular cross section is proportional to the product xy3. Find the stiffest beam which can be cut from a log with diameter d = 14 inches. See figure on right.

A sheet of cardboard 30 in square is used to make an open box by cutting squares of equal size from the corners and folding up the sides. What size squares should be cut to obtain a box with largest possible volume?

Determine the x-coordinate of each stationary point of f(x) = 3x2 -24x.

The position function of a particle is given by s(t) = 4t - 3t2 + 4t3. Find the velocity function.

If f(x) = (x - 7)4 + 3 , find the location of any inflection points.

A line is drawn through the point P(5, 2) so that it intersects the y-axis at A(0,y) and the x-axis at B(x,0). Find the smallest triangle formed if x and y are positive.

The largest interval over which f is increasing for f(x) = x9 - 5 is

Sketch the graph of y = 7x4 -7x3 + 2. Find any stationary points and any points of inflection.

Answer true or false. Using a graphing utility it can be shown that f(x) = x4 sin 4x has a relative maximum on 0 < x < 2 π\piπ .

Answer true or false. A fence is to be used to enclose a rectangular plot of land. If there are 920 feet of fencing, it can be shown that a 230 ft by 230 ft square is the rectangle that can be enclosed with the greatest area. (A square is considered a rectangle.)

If f(x) = sin 2x (0, π\piπ ), find the intervals where f is concave up and where f is concave down.

The position function of a particle is given by s(t) = 8t + cos t. Find the velocity function.

Verify that f(x) = x3 - 5x + 3 satisfies the hypothesis of the Mean-Value Theorem over the interval [-2, 3] and find all values of C that satisfy the conclusion of the theorem.

If f(x) = 3x4 -90x2 , find the intervals where f is concave up and where f is concave down.

Answer true or false. f(x) = | cot2x| has no relative extrema on .

Given . Find any stationary points and any points of inflection. Also find any vertical and horizontal asymptotes.

Let s(t) = t4 - 5t + 6 be a position function. The acceleration function a(t) =

Answer true or false. If f ''(-8) = -10 and f ''(8) = 10, then there must be a point of inflection on (-8, 8).

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

Approximate by applying Newton's Method to the equation x³ - 88 = 0. Use 4 for your initial value and calculate nine iterations.

If f(x) = 9x⁴ - 6x³ + 1 , find the inflection points.

The stiffness of a beam of rectangular cross section is proportional to the product xy³. Find the stiffest beam which can be cut from a log with diameter d = 14 inches. See figure on right.

Determine the x-coordinate of each stationary point of f(x) = 3x² -24x.

The position function of a particle is given by s(t) = 4t - 3t² + 4t³. Find the velocity function.

If f(x) = (x - 7)⁴ + 3 , find the location of any inflection points.

The largest interval over which f is increasing for f(x) = x⁹ - 5 is

Sketch the graph of y = 7x⁴ -7x³ + 2. Find any stationary points and any points of inflection.

Answer true or false. Using a graphing utility it can be shown that f(x) = x⁴ sin 4x has a relative maximum on 0 < x < 2 $\pi$ .

If f(x) = sin 2x (0, $\pi$ ), find the intervals where f is concave up and where f is concave down.

Verify that f(x) = x³ - 5x + 3 satisfies the hypothesis of the Mean-Value Theorem over the interval [-2, 3] and find all values of C that satisfy the conclusion of the theorem.

If f(x) = 3x⁴ -90x²_,find the intervals where f is concave up and where f is concave down.

Answer true or false. f(x) = | cot²x| has no relative extrema on .

Let s(t) = t⁴ - 5t + 6 be a position function. The acceleration function a(t) =