Question 1

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

Accepted Answer

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

Question 2

Find the extreme values for   on the interval (0, 2) and determine where those values occur.

Accepted Answer

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

Question 3

Find the relative extrema for   .

Accepted Answer

Relative minimum at (1, -1)
[C

Question 4

Use a graphing utility to estimate the absolute minimum of f(x) = ln(x8) on [1, 3].

Accepted Answer

Question 5

If f(x) = x4 - 4x2, find the intervals where f is increasing and where f is decreasing.

Accepted Answer

Increasing on (-

Question 6

Answer true or false. f(x) = | sec2x| has no relative extrema on   .

Accepted Answer

A) True 
 B)False

Question 7

Find the relative extrema for f(x) = 9x2/3 - 4x.

Accepted Answer

Relative m

Question 8

f(x) = 9x4 - 7x5 , find the intervals where f is increasing and where f is decreasing.

Accepted Answer

Increasing

Question 9

A company has a cost of operation function given by C(t) = 0.02t2 - 2t + 5,000 for 0 $\le$  t $\le$  500. Find the minimum cost of operation.

Accepted Answer

A)  5,000 
B)  4,950 
C)  9,900 
D)  4,999.96 
E)  4901 
A)  5,000 
B)  4,950 
C)  9,900 
D)  4,999.96 
E)  4901

Question 10

A can containing 13.5 in3 of tuna and water is to be made in the form of a circular cylinder. What dimensions of the can will require the least amount of material? (V =  $\pi$r2h, S = 2 $\pi$rh, A =  $\pi$r2)

Accepted Answer

V = @#LAT-DLM&r²h = 13.5, so

Question 11

Use Newton's Method to find the largest positive solution of x4 + x3 -4x2- 4x - 7 = 0.

Accepted Answer

A)  3.1305970 
B)  2.5780547 
C)  2.2297942 
D)  2.3053804 
E)  2.2343687 
A)  3.1305970 
B)  2.5780547 
C)  2.2297942 
D)  2.3053804 
E)  2.2343687

Question 12

Sketch the graph of   . Find any stationary points and any points of inflection. Also find any vertical and horizontal asymptotes.

Accepted Answer

@#IMG-DLM& @#IMG-DLM& No relative minima

Question 13

Two fences, a distance of d = 16 feet apart are to be constructed so that the first fence is a height of h = 2 feet high and the second fence is higher than the first. What is the length of the shortest pole that has one end on the ground, passing over the first fence and reaches the second fence? See figure.

Accepted Answer

Let x = AB + BC so that x = 2 csc @#LAT-DLM& + 16

Question 14

Answer true or false. The Mean-Value Theorem guarantees there is at least one c on [0, 3] such that f '(x) = 0.9 when f(x) = x.

Accepted Answer

A) True 
 B)False

Question 15

Answer true or false. The hypotheses of the Mean-Value Theorem are satisfied for f(x) = cos 2x on [0, 4 $\pi$].

Accepted Answer

A) True 
 B)False

Question 16

Answer true or false. A point that has an x-coordinate where f ''(x) = 0 is a point of inflection.

Accepted Answer

A) True 
 B)False

Question 17

f(x) = 4x4 - 9x5 , find the intervals where f is increasing and where f is decreasing.

Accepted Answer

Increasing

Question 18

The position function of a particle is given by s(t) = 9t - 9. Find the velocity function.

Accepted Answer

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

Question 19

On a [-10, 10] by [-10, 10] window on a graphing utility the rational function   has

Accepted Answer

A)  one horizontal asymptote; no vertical asymptote 
B)  no horizontal asymptote; one vertical asymptote 
C)  one horizontal asymptote; two vertical asymptote 
D)  one horizontal asymptote; three vertical asymptotes 
E)  one horizontal asymptote; one vertical asymptotes 
A)  one horizontal asymptote; no vertical asymptote 
B)  no horizontal asymptote; one vertical asymptote 
C)  one horizontal asymptote; two vertical asymptote 
D)  one horizontal asymptote; three vertical asymptotes 
E)  one horizontal asymptote; one vertical asymptotes

Question 20

Answer true or false. f(x) = 4xe 2x has a relative minimum.

Accepted Answer

A) True 
 B)False

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

Find the extreme values for on the interval (0, 2) and determine where those values occur.

Find the relative extrema for .

Use a graphing utility to estimate the absolute minimum of f(x) = ln(x⁸) on [1, 3].

If f(x) = x⁴ - 4x², find the intervals where f is increasing and where f is decreasing.

Answer true or false. f(x) = | sec²x| has no relative extrema on .

Find the relative extrema for f(x) = 9x^2/3 - 4x.

f(x) = 9x⁴ - 7x⁵ , find the intervals where f is increasing and where f is decreasing.

A company has a cost of operation function given by C(t) = 0.02t² - 2t + 5,000 for 0 $\le$ t $\le$ 500. Find the minimum cost of operation.

A can containing 13.5 in³ of tuna and water is to be made in the form of a circular cylinder. What dimensions of the can will require the least amount of material? (V = $\pi$ r²h, S = 2 $\pi$ rh, A = $\pi$ r²)

Use Newton's Method to find the largest positive solution of x⁴ + x³ -4x²- 4x - 7 = 0.

Sketch the graph of . Find any stationary points and any points of inflection. Also find any vertical and horizontal asymptotes.

Answer true or false. The Mean-Value Theorem guarantees there is at least one c on [0, 3] such that f '(x) = 0.9 when f(x) = x.

Answer true or false. The hypotheses of the Mean-Value Theorem are satisfied for f(x) = cos 2x on [0, 4 $\pi$ ].

Answer true or false. A point that has an x-coordinate where f ''(x) = 0 is a point of inflection.

f(x) = 4x⁴ - 9x⁵ , find the intervals where f is increasing and where f is decreasing.

The position function of a particle is given by s(t) = 9t - 9. Find the velocity function.

On a [-10, 10] by [-10, 10] window on a graphing utility the rational function has

Answer true or false. f(x) = 4xe ²^x has a relative minimum.

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

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

Find the extreme values for on the interval (0, 2) and determine where those values occur.

Find the relative extrema for .

Use a graphing utility to estimate the absolute minimum of f(x) = ln(x8) on [1, 3].

If f(x) = x4 - 4x2, find the intervals where f is increasing and where f is decreasing.

Answer true or false. f(x) = | sec2x| has no relative extrema on .

Find the relative extrema for f(x) = 9x2/3 - 4x.

f(x) = 9x4 - 7x5 , find the intervals where f is increasing and where f is decreasing.

A company has a cost of operation function given by C(t) = 0.02t2 - 2t + 5,000 for 0 ≤\le≤ t ≤\le≤ 500. Find the minimum cost of operation.

A can containing 13.5 in3 of tuna and water is to be made in the form of a circular cylinder. What dimensions of the can will require the least amount of material? (V = π\piπ r2h, S = 2 π\piπ rh, A = π\piπ r2)

Use Newton's Method to find the largest positive solution of x4 + x3 -4x2- 4x - 7 = 0.

Sketch the graph of . Find any stationary points and any points of inflection. Also find any vertical and horizontal asymptotes.

Answer true or false. The Mean-Value Theorem guarantees there is at least one c on [0, 3] such that f '(x) = 0.9 when f(x) = x.

Answer true or false. The hypotheses of the Mean-Value Theorem are satisfied for f(x) = cos 2x on [0, 4 π\piπ ].

Answer true or false. A point that has an x-coordinate where f ''(x) = 0 is a point of inflection.

f(x) = 4x4 - 9x5 , find the intervals where f is increasing and where f is decreasing.

The position function of a particle is given by s(t) = 9t - 9. Find the velocity function.

On a [-10, 10] by [-10, 10] window on a graphing utility the rational function has

Answer true or false. f(x) = 4xe 2x has a relative minimum.

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

Use a graphing utility to estimate the absolute minimum of f(x) = ln(x⁸) on [1, 3].

If f(x) = x⁴ - 4x², find the intervals where f is increasing and where f is decreasing.

Answer true or false. f(x) = | sec²x| has no relative extrema on .

Find the relative extrema for f(x) = 9x^2/3 - 4x.

f(x) = 9x⁴ - 7x⁵ , find the intervals where f is increasing and where f is decreasing.

A company has a cost of operation function given by C(t) = 0.02t² - 2t + 5,000 for 0 $\le$ t $\le$ 500. Find the minimum cost of operation.

A can containing 13.5 in³ of tuna and water is to be made in the form of a circular cylinder. What dimensions of the can will require the least amount of material? (V = $\pi$ r²h, S = 2 $\pi$ rh, A = $\pi$ r²)

Use Newton's Method to find the largest positive solution of x⁴ + x³ -4x²- 4x - 7 = 0.

Answer true or false. The hypotheses of the Mean-Value Theorem are satisfied for f(x) = cos 2x on [0, 4 $\pi$ ].

f(x) = 4x⁴ - 9x⁵ , find the intervals where f is increasing and where f is decreasing.

Answer true or false. f(x) = 4xe ²^x has a relative minimum.