Question 1

Find the relative extreme values for f(x) = x - sin x on the interval   and determine where those values occur.

Accepted Answer

f '(x) = 1 - cos x ;

Question 2

A rectangular sheet of cardboard 64 cm by 93 cm is used to make an open box by cutting squares of equal size from the four corners and folding up the sides. What size squares should be cut to obtain the largest possible volume?

Accepted Answer

A)    
B)    
C)    
D)  4 
E)    
A)    
B)    
C)    
D)  4 
E)

Question 3

Use a graphing utility to estimate the absolute maximum of f(x) = -(ln x)6 on [1, 10].

Accepted Answer

Question 4

Sketch the graph of   . Find all vertical, horizontal, and oblique asymptotes.

Accepted Answer

@#IMG-DLM& so y = x

Question 5

Answer true or false. The hypotheses of the Mean-Value Theorem are satisfied for   on [0, 8 $\pi$].

Accepted Answer

A) True 
 B)False

Question 6

If f(x) = 5x4 -5x3 + 19 , find the intervals where f is increasing and where f is decreasing.

Accepted Answer

Increasing

Question 7

Sketch the graph of y = 6x4 -3x3 + 2. Find any stationary points and any points of inflection.

Accepted Answer

y' = 24x³ - 9x

Question 8

Answer true or false. Rolle's Theorem is used to find the zeros of a function.

Accepted Answer

A) True 
 B)False

Question 9

If f(x) = 5x4 - 11x3 + 18 , find the intervals where f is concave up and where f is concave down.

Accepted Answer

Concave up

Question 10

If f(x) = x(x - 12)2 , find the intervals where f is concave up and where f is concave down.

Accepted Answer

The answer of If f(x) = x(x - 12)2 ,...

Question 11

Given f(x) = -4x3 + 24x2 . Use a graphing utility to estimate the absolute maximum and minimum values of f, if any, on the interval [0, 6].

Accepted Answer

Absolute maximum of

Question 12

Use a graphing utility to estimate the absolute maximum of f(x) = -e4x on [-3, 3]. at

Accepted Answer

Question 13

f(x) = x2 + 12x + 9 has a

Accepted Answer

A)  relative maximum at x = -6 
B)  relative minimum at x = -6 
C)  relative maximum at x = -12 
D)  relative minimum at x = -12 
E)  relative maximum at x = -9 
A)  relative maximum at x = -6 
B)  relative minimum at x = -6 
C)  relative maximum at x = -12 
D)  relative minimum at x = -12 
E)  relative maximum at x = -9

Question 14

Find the relative extrema for f(x) = (x + 1)-1/5.

Accepted Answer

@#IMG-DLM& No critical points,

Question 15

Find the value of c in the interval [-1, 1] that satisfies the Mean Value Theorem. f(x) = x2 - 4x + 3

Accepted Answer

f(1) = 1² - 4(1) +

Question 16

Sketch the graph of   . Find any stationary points.

Accepted Answer

@#IMG-DLM& @#IMG-DLM& Vertical assymptot

Question 17

Verify that   satisfies the hypothesis of the Mean-Value Theorem over the interval [6, 8] and find all values of C that satisfy the conclusion of the theorem.

Accepted Answer

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

Question 18

Answer true or false. f(x) = sin 2x cos 2x on   has an absolute maximum at   .

Accepted Answer

A) True 
 B)False

Question 19

The absolute minimum of   occurs at x =

Accepted Answer

A)  0 
B)  64 
C)  8 
D)  -8 
E)  None exists 
A)  0 
B)  64 
C)  8 
D)  -8 
E)  None exists

Question 20

The equation, x3 + x2 - 4x - 8 = 0 has one real solution for 1 < x < 8. Approximate it by Newton's Method.

Accepted Answer

f(x) = x³+x

Find the relative extreme values for f(x) = x - sin x on the interval and determine where those values occur.

A rectangular sheet of cardboard 64 cm by 93 cm is used to make an open box by cutting squares of equal size from the four corners and folding up the sides. What size squares should be cut to obtain the largest possible volume?

Use a graphing utility to estimate the absolute maximum of f(x) = -(ln x)⁶ on [1, 10].

Sketch the graph of . Find all vertical, horizontal, and oblique asymptotes.

Answer true or false. The hypotheses of the Mean-Value Theorem are satisfied for $Answer true or false. The hypotheses of the Mean-Value Theorem are satisfied for on [0, 8 \pi ].$ on [0, 8 $\pi$ ].

If f(x) = 5x⁴ -5x³ + 19 , find the intervals where f is increasing and where f is decreasing.

Sketch the graph of y = 6x⁴ -3x³ + 2. Find any stationary points and any points of inflection.

Answer true or false. Rolle's Theorem is used to find the zeros of a function.

If f(x) = 5x⁴ - 11x³ + 18 , find the intervals where f is concave up and where f is concave down.

If f(x) = x(x - 12)² , find the intervals where f is concave up and where f is concave down.

Given f(x) = -4x³ + 24x² . Use a graphing utility to estimate the absolute maximum and minimum values of f, if any, on the interval [0, 6].

Use a graphing utility to estimate the absolute maximum of f(x) = -e⁴^x on [-3, 3]. at

f(x) = x² + 12x + 9 has a

Find the relative extrema for f(x) = (x + 1)^-^1/5.

Find the value of c in the interval [-1, 1] that satisfies the Mean Value Theorem. f(x) = x² - 4x + 3

Sketch the graph of . Find any stationary points.

Verify that satisfies the hypothesis of the Mean-Value Theorem over the interval [6, 8] and find all values of C that satisfy the conclusion of the theorem.

Answer true or false. f(x) = sin 2x cos 2x on has an absolute maximum at .

The absolute minimum of occurs at x =

The equation, x³ + x²- 4x - 8 = 0 has one real solution for 1 < x < 8. Approximate it by Newton's Method.

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

Find the relative extreme values for f(x) = x - sin x on the interval and determine where those values occur.

A rectangular sheet of cardboard 64 cm by 93 cm is used to make an open box by cutting squares of equal size from the four corners and folding up the sides. What size squares should be cut to obtain the largest possible volume?

Use a graphing utility to estimate the absolute maximum of f(x) = -(ln x)6 on [1, 10].

Sketch the graph of . Find all vertical, horizontal, and oblique asymptotes.

Answer true or false. The hypotheses of the Mean-Value Theorem are satisfied for on [0, 8 π\piπ ].

If f(x) = 5x4 -5x3 + 19 , find the intervals where f is increasing and where f is decreasing.

Sketch the graph of y = 6x4 -3x3 + 2. Find any stationary points and any points of inflection.

Answer true or false. Rolle's Theorem is used to find the zeros of a function.

If f(x) = 5x4 - 11x3 + 18 , find the intervals where f is concave up and where f is concave down.

If f(x) = x(x - 12)2 , find the intervals where f is concave up and where f is concave down.

Given f(x) = -4x3 + 24x2 . Use a graphing utility to estimate the absolute maximum and minimum values of f, if any, on the interval [0, 6].

Use a graphing utility to estimate the absolute maximum of f(x) = -e4x on [-3, 3]. at

f(x) = x2 + 12x + 9 has a

Find the relative extrema for f(x) = (x + 1)-1/5.

Find the value of c in the interval [-1, 1] that satisfies the Mean Value Theorem. f(x) = x2 - 4x + 3

Sketch the graph of . Find any stationary points.

Verify that satisfies the hypothesis of the Mean-Value Theorem over the interval [6, 8] and find all values of C that satisfy the conclusion of the theorem.

Answer true or false. f(x) = sin 2x cos 2x on has an absolute maximum at .

The absolute minimum of occurs at x =

The equation, x3 + x2 - 4x - 8 = 0 has one real solution for 1 < x < 8. Approximate it by Newton's Method.

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 maximum of f(x) = -(ln x)⁶ on [1, 10].

Answer true or false. The hypotheses of the Mean-Value Theorem are satisfied for $Answer true or false. The hypotheses of the Mean-Value Theorem are satisfied for on [0, 8 \pi ].$ on [0, 8 $\pi$ ].

If f(x) = 5x⁴ -5x³ + 19 , find the intervals where f is increasing and where f is decreasing.

Sketch the graph of y = 6x⁴ -3x³ + 2. Find any stationary points and any points of inflection.

If f(x) = 5x⁴ - 11x³ + 18 , find the intervals where f is concave up and where f is concave down.

If f(x) = x(x - 12)² , find the intervals where f is concave up and where f is concave down.

Given f(x) = -4x³ + 24x² . Use a graphing utility to estimate the absolute maximum and minimum values of f, if any, on the interval [0, 6].

Use a graphing utility to estimate the absolute maximum of f(x) = -e⁴^x on [-3, 3]. at

f(x) = x² + 12x + 9 has a

Find the relative extrema for f(x) = (x + 1)^-^1/5.

Find the value of c in the interval [-1, 1] that satisfies the Mean Value Theorem. f(x) = x² - 4x + 3

The equation, x³ + x²- 4x - 8 = 0 has one real solution for 1 < x < 8. Approximate it by Newton's Method.