Question 1

Let s(t) = t3 - t be a position function of a particle. At 4 the particle's acceleration is

Accepted Answer

A)  negative 
B)  positive 
C)  zero 
A)  negative 
B)  positive 
C)  zero

Question 2

On the interval (0, 2 $\pi$), f(x) = | sin x cos(9x)| has

Accepted Answer

A)  a relative maximum only 
B)  a relative minimum only 
C)  both a relative maximum and a relative minimum 
D)  no relative extrema 
E)  cannot be determined 
A)  a relative maximum only 
B)  a relative minimum only 
C)  both a relative maximum and a relative minimum 
D)  no relative extrema 
E)  cannot be determined

Question 3

A slice of pizza, in the form of a sector of a circle, is to have a perimeter of 18 inches. What should be the radius of the pan to make the slice of pizza largest.
(The area of a sector of a circle,   where $\theta$ is the central angle in radians and the arc length along a circle is S = r$\theta$with $\theta$ in radians.)

Accepted Answer

Let r and @#LAT-DLM& be as shown in the diagram. T

Question 4

Verify that f(x) = x3 -3x2- 3x + 1 satisfies the hypothesis of the Mean-Value Theorem over the interval [0, 2] and find all values of C that satisfy the conclusion of the theorem.

Accepted Answer

f(0) = 1
f(2) = -9
f '(x) = 3x

Question 5

A poster is to contain 240 in2 of printed matter with margins of 3 in. each at top and bottom and 2 in. at each side. Find the overall dimensions if the total area of the poster is to be a minimum.

Accepted Answer

Let the original area be 240 =

Question 6

Answer true or false. tan(-x + 6) has a point of inflection on   .

Accepted Answer

A) True 
 B)False

Question 7

If f(x) = 2x4 -17x3 , find the intervals where f is increasing and where f is decreasing.

Accepted Answer

Increasing

Question 8

Use a graphing utility to locate the value of x where f(x) = x4- 3x + 11 has an absolute minimum, if it exists.

Accepted Answer

A)  1 
B)    
C)  0 
D)  None exists 
E)  -11 
A)  1 
B)    
C)  0 
D)  None exists 
E)  -11

Question 9

The function f(x) = x9 - 9 has a point of inflection with an x-coordinate of

Accepted Answer

A)  9 
B)  -9 
C)  0 
D)  None exist 
A)  9 
B)  -9 
C)  0 
D)  None exist

Question 10

Find the relative extrema for f(x) = x4 - 4x2 + 5.

Accepted Answer

f '(x) = 4x(x² - 2)

Question 11

Find the extreme values for f(x) = 4x4/3 -6x1/3 on the interval [-1, 8] and determine where those values occur.

Accepted Answer

@#IMG-DLM& ; f '(x) = 0 when @#IMG-DLM& and f '(x)

Question 12

Find the value c that satisfies the Mean-Value Theorem for f(x) = x3 = 0 on [0, 7].

Accepted Answer

A)    
B)    
C)  7 
D)  0 
E)    
A)    
B)    
C)  7 
D)  0 
E)

Question 13

Find the circular cylinder of largest lateral area which can be inscribed in a sphere of radius R = 4 feet. [Surface area of a cylinder, S = 2 $\pi$rh, where r = radius, h = height.]

Accepted Answer

The answer of Find the circular cylinder of largest lateral...

Question 14

Answer true or false. An object thrown upward reaches a height of s(t) = -9.8t2 + 39.2t. The object is highest at t = 2, where t is in seconds?

Accepted Answer

A) True 
 B)False

Question 15

Find the extreme values for   on the interval [-2, 4] and determine where those values occur.

Accepted Answer

@#IMG-DLM& ; f '(x) = 0 when x = 0
Relat

Question 16

The cost of fuel used in propelling a dirigible varies as the square of its speed and is $100/hour when the speed is 100 miles/hour. Other expenses amount to $400/hour. Find the most economical speed for a voyage of 1,100 miles.

Accepted Answer

Let x be the speed of the dirigible and

Question 17

If f(x) = x4 . Use a graphing utility to estimate the absolute maximum and minimum values of f, if any, on the interval [-1, 5].

Accepted Answer

Absolute minimum of

Question 18

f(x) = 4x4 - 7x5 , find the intervals where f is concave up and where f is concave down.

Accepted Answer

Concave up

Question 19

If f(x) = 6x4- 4x3 + 11 , find the intervals where f is concave up and where f is concave down.

Accepted Answer

Concave up

Question 20

Let s(t) = 3t4. Find t when a = 0.

Accepted Answer

A)  4 
B)  36 
C)  0 
D)  12 
E)  2 
A)  4 
B)  36 
C)  0 
D)  12 
E)  2

Let s(t) = t³ - t be a position function of a particle. At 4 the particle's acceleration is

On the interval (0, 2 $\pi$ ), f(x) = | sin x cos(9x)| has

Verify that f(x) = x³ -3x²- 3x + 1 satisfies the hypothesis of the Mean-Value Theorem over the interval [0, 2] and find all values of C that satisfy the conclusion of the theorem.

A poster is to contain 240 in² of printed matter with margins of 3 in. each at top and bottom and 2 in. at each side. Find the overall dimensions if the total area of the poster is to be a minimum.

Answer true or false. tan(-x + 6) has a point of inflection on .

If f(x) = 2x⁴ -17x³ , find the intervals where f is increasing and where f is decreasing.

Use a graphing utility to locate the value of x where f(x) = x⁴- 3x + 11 has an absolute minimum, if it exists.

The function f(x) = x⁹ - 9 has a point of inflection with an x-coordinate of

Find the relative extrema for f(x) = x⁴ - 4x² + 5.

Find the extreme values for f(x) = 4x^4/3 -6x^1/3 on the interval [-1, 8] and determine where those values occur.

Find the value c that satisfies the Mean-Value Theorem for f(x) = x³ = 0 on [0, 7].

Find the circular cylinder of largest lateral area which can be inscribed in a sphere of radius R = 4 feet. [Surface area of a cylinder, S = 2 $\pi$ rh, where r = radius, h = height.]

Answer true or false. An object thrown upward reaches a height of s(t) = -9.8t² + 39.2t. The object is highest at t = 2, where t is in seconds?

Find the extreme values for on the interval [-2, 4] and determine where those values occur.

The cost of fuel used in propelling a dirigible varies as the square of its speed and is $100/hour when the speed is 100 miles/hour. Other expenses amount to $400/hour. Find the most economical speed for a voyage of 1,100 miles.

If f(x) = x⁴ . Use a graphing utility to estimate the absolute maximum and minimum values of f, if any, on the interval [-1, 5].

f(x) = 4x⁴ - 7x⁵ , find the intervals where f is concave up and where f is concave down.

If f(x) = 6x⁴- 4x³ + 11 , find the intervals where f is concave up and where f is concave down.

Let s(t) = 3t⁴. Find t when a = 0.

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

Let s(t) = t3 - t be a position function of a particle. At 4 the particle's acceleration is

On the interval (0, 2 π\piπ ), f(x) = | sin x cos(9x)| has

Verify that f(x) = x3 -3x2- 3x + 1 satisfies the hypothesis of the Mean-Value Theorem over the interval [0, 2] and find all values of C that satisfy the conclusion of the theorem.

A poster is to contain 240 in2 of printed matter with margins of 3 in. each at top and bottom and 2 in. at each side. Find the overall dimensions if the total area of the poster is to be a minimum.

Answer true or false. tan(-x + 6) has a point of inflection on .

If f(x) = 2x4 -17x3 , find the intervals where f is increasing and where f is decreasing.

Use a graphing utility to locate the value of x where f(x) = x4- 3x + 11 has an absolute minimum, if it exists.

The function f(x) = x9 - 9 has a point of inflection with an x-coordinate of

Find the relative extrema for f(x) = x4 - 4x2 + 5.

Find the extreme values for f(x) = 4x4/3 -6x1/3 on the interval [-1, 8] and determine where those values occur.

Find the value c that satisfies the Mean-Value Theorem for f(x) = x3 = 0 on [0, 7].

Find the circular cylinder of largest lateral area which can be inscribed in a sphere of radius R = 4 feet. [Surface area of a cylinder, S = 2 π\piπ rh, where r = radius, h = height.]

Answer true or false. An object thrown upward reaches a height of s(t) = -9.8t2 + 39.2t. The object is highest at t = 2, where t is in seconds?

Find the extreme values for on the interval [-2, 4] and determine where those values occur.

The cost of fuel used in propelling a dirigible varies as the square of its speed and is $100/hour when the speed is 100 miles/hour. Other expenses amount to $400/hour. Find the most economical speed for a voyage of 1,100 miles.

If f(x) = x4 . Use a graphing utility to estimate the absolute maximum and minimum values of f, if any, on the interval [-1, 5].

f(x) = 4x4 - 7x5 , find the intervals where f is concave up and where f is concave down.

If f(x) = 6x4- 4x3 + 11 , find the intervals where f is concave up and where f is concave down.

Let s(t) = 3t4. Find t when a = 0.

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

Let s(t) = t³ - t be a position function of a particle. At 4 the particle's acceleration is

On the interval (0, 2 $\pi$ ), f(x) = | sin x cos(9x)| has

Verify that f(x) = x³ -3x²- 3x + 1 satisfies the hypothesis of the Mean-Value Theorem over the interval [0, 2] and find all values of C that satisfy the conclusion of the theorem.

A poster is to contain 240 in² of printed matter with margins of 3 in. each at top and bottom and 2 in. at each side. Find the overall dimensions if the total area of the poster is to be a minimum.

If f(x) = 2x⁴ -17x³ , find the intervals where f is increasing and where f is decreasing.

Use a graphing utility to locate the value of x where f(x) = x⁴- 3x + 11 has an absolute minimum, if it exists.

The function f(x) = x⁹ - 9 has a point of inflection with an x-coordinate of

Find the relative extrema for f(x) = x⁴ - 4x² + 5.

Find the extreme values for f(x) = 4x^4/3 -6x^1/3 on the interval [-1, 8] and determine where those values occur.

Find the value c that satisfies the Mean-Value Theorem for f(x) = x³ = 0 on [0, 7].

Find the circular cylinder of largest lateral area which can be inscribed in a sphere of radius R = 4 feet. [Surface area of a cylinder, S = 2 $\pi$ rh, where r = radius, h = height.]

Answer true or false. An object thrown upward reaches a height of s(t) = -9.8t² + 39.2t. The object is highest at t = 2, where t is in seconds?

If f(x) = x⁴ . Use a graphing utility to estimate the absolute maximum and minimum values of f, if any, on the interval [-1, 5].

f(x) = 4x⁴ - 7x⁵ , find the intervals where f is concave up and where f is concave down.

If f(x) = 6x⁴- 4x³ + 11 , find the intervals where f is concave up and where f is concave down.

Let s(t) = 3t⁴. Find t when a = 0.