Question 1

Use a graphing utility to estimate the absolute minimum of f(x) = (ln x)(x - 3)2 on the interval (1, 5).

Accepted Answer

0 at x = 3

Question 2

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 3

Verify that f(x) = x2 + 2 satisfies the hypothesis of the Mean-Value Theorem on the interval [0, 4] and find all values of C that satisfy the conclusion of the theorem.

Accepted Answer

f(0) = 2
f

Question 4

Given y = x2/3(x + 6). Plot any stationary points, inflections points, and cusps which may or may not exist. Approximate answers to 4 decimal places.

Accepted Answer

@#IMG-DLM& @#IMG-DLM& Relative maximum at (-2.4, @#IMG-DLM&

Question 5

For a triangle with sides 6 m, 8 m, and 10 m, the smallest circle that contains the triangle has a diameter of

Accepted Answer

A)  6 m 
B)  8 m 
C)  10 m 
D)  14 m 
E)  12 m 
A)  6 m 
B)  8 m 
C)  10 m 
D)  14 m 
E)  12 m

Question 6

Use a graphing utility to assist in determining the location of the absolute maximum of f(x) = -(x2 - 7)2 on (-$\infty$, $\infty$), if it exists.

Accepted Answer

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

Question 7

f(x) = |x2 - 9| has

Accepted Answer

A)  no relative maximum and a relative minimum at x = 3 
B)  a relative maximum at x = 3 and no relative minimum. 
C)  relative minima at x = -3 and x = 3; a relative maximum at x = 0 
D)  relative maxima at x = -3 and x = 3; a relative minimum at x = 0 
E)  no relative extrema 
A)  no relative maximum and a relative minimum at x = 3 
B)  a relative maximum at x = 3 and no relative minimum. 
C)  relative minima at x = -3 and x = 3; a relative maximum at x = 0 
D)  relative maxima at x = -3 and x = 3; a relative minimum at x = 0 
E)  no relative extrema

Question 8

Find the relative extreme values for f(x) = 5x3 - 30x2 + 7 on the interval [-1, 10] and determine where those values occur.

Accepted Answer

f '(x) = 15x² - 60x

Question 9

Answer true or false. All functions of the form f(x) = axn , where n is odd and a$\neq$ 0 have an inflection point.

Accepted Answer

A) True 
 B)False

Question 10

Given f(x) = -5x3 + 15x2 . Use a graphing utility to estimate the absolute maximum and minimum values of f, if any, on the interval [0, 3].

Accepted Answer

Absolute maximum of

Question 11

Find all relative extrema of f(x) = x4/7.

Accepted Answer

Relative m

Question 12

Find the extreme values for f(x) = x - sin 4x on the interval   and determine where those values occur.

Accepted Answer

f '(x) = 1 - 4 cos 4x ; Critic

Question 13

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

Accepted Answer

Vertical asymptote a

Question 14

Find the relative extreme values for f(x) = 3x3 -18x2 + 2 on the interval [-1, 10] and determine where those values occur.

Accepted Answer

f '(x) = 9x² - 36x

Question 15

The strength of a beam with a rectangular cross section varies directly as x and as the square of y. What are the dimensions of the strongest beam that can be sawed out of a round log whose diameter is d = 27 inches? See figure on right.

Accepted Answer

The answer of The strength of a beam with a...

Question 16

Answer true or false. The hypotheses of the Mean-Value Theorem are satisfied for   on [-1, 1].

Accepted Answer

A) True 
 B)False

Question 17

Express the number 54 as the sum of two nonnegative numbers whose product is as large as possible.

Accepted Answer

A)  0, 54 
B)  20, 34 
C)  27, 27 
D)  6, 48 
E)  16, 38 
A)  0, 54 
B)  20, 34 
C)  27, 27 
D)  6, 48 
E)  16, 38

Question 18

Determine which function is graphed.

Accepted Answer

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

Question 19

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 $200/hour. Find the most economical speed for a voyage of 1,400 miles.

Accepted Answer

Let x be the speed of the dirigible and

Question 20

A lighthouse is 8 miles off a straight coast and a town is located 18 miles down the seacoast. Supplies are to be moved from the town to the lighthouse on a regular basis and at a minimum time. If the supplies can be moved at the rate of 7 miles/hour on water and 25 miles/hour over land, how far from the town should a dock be constructed for shipment of supplies?

Accepted Answer

@#IMG-DLM& The dock

Use a graphing utility to estimate the absolute minimum of f(x) = (ln x)(x - 3)² on the interval (1, 5).

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

Verify that f(x) = x² + 2 satisfies the hypothesis of the Mean-Value Theorem on the interval [0, 4] and find all values of C that satisfy the conclusion of the theorem.

Given y = x^2/3(x + 6). Plot any stationary points, inflections points, and cusps which may or may not exist. Approximate answers to 4 decimal places.

For a triangle with sides 6 m, 8 m, and 10 m, the smallest circle that contains the triangle has a diameter of

Use a graphing utility to assist in determining the location of the absolute maximum of f(x) = -(x² - 7)² on (- $\infty$ , $\infty$ ), if it exists.

f(x) = |x² - 9| has

Find the relative extreme values for f(x) = 5x³ - 30x² + 7 on the interval [-1, 10] and determine where those values occur.

Answer true or false. All functions of the form f(x) = axⁿ , where n is odd and a $\neq$ 0 have an inflection point.

Given f(x) = -5x³ + 15x² . Use a graphing utility to estimate the absolute maximum and minimum values of f, if any, on the interval [0, 3].

Find all relative extrema of f(x) = x⁴^/⁷.

Find the extreme values for f(x) = x - sin 4x on the interval and determine where those values occur.

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

Find the relative extreme values for f(x) = 3x³ -18x² + 2 on the interval [-1, 10] and determine where those values occur.

The strength of a beam with a rectangular cross section varies directly as x and as the square of y. What are the dimensions of the strongest beam that can be sawed out of a round log whose diameter is d = 27 inches? See figure on right.

Answer true or false. The hypotheses of the Mean-Value Theorem are satisfied for on [-1, 1].

Express the number 54 as the sum of two nonnegative numbers whose product is as large as possible.

Determine which function is graphed.

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 $200/hour. Find the most economical speed for a voyage of 1,400 miles.

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 minimum of f(x) = (ln x)(x - 3)2 on the interval (1, 5).

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

Verify that f(x) = x2 + 2 satisfies the hypothesis of the Mean-Value Theorem on the interval [0, 4] and find all values of C that satisfy the conclusion of the theorem.

Given y = x2/3(x + 6). Plot any stationary points, inflections points, and cusps which may or may not exist. Approximate answers to 4 decimal places.

For a triangle with sides 6 m, 8 m, and 10 m, the smallest circle that contains the triangle has a diameter of

Use a graphing utility to assist in determining the location of the absolute maximum of f(x) = -(x2 - 7)2 on (- ∞\infty∞ , ∞\infty∞ ), if it exists.

f(x) = |x2 - 9| has

Find the relative extreme values for f(x) = 5x3 - 30x2 + 7 on the interval [-1, 10] and determine where those values occur.

Answer true or false. All functions of the form f(x) = axn , where n is odd and a ≠\neq= 0 have an inflection point.

Given f(x) = -5x3 + 15x2 . Use a graphing utility to estimate the absolute maximum and minimum values of f, if any, on the interval [0, 3].

Find all relative extrema of f(x) = x4/7.

Find the extreme values for f(x) = x - sin 4x on the interval and determine where those values occur.

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

Find the relative extreme values for f(x) = 3x3 -18x2 + 2 on the interval [-1, 10] and determine where those values occur.

The strength of a beam with a rectangular cross section varies directly as x and as the square of y. What are the dimensions of the strongest beam that can be sawed out of a round log whose diameter is d = 27 inches? See figure on right.

Answer true or false. The hypotheses of the Mean-Value Theorem are satisfied for on [-1, 1].

Express the number 54 as the sum of two nonnegative numbers whose product is as large as possible.

Determine which function is graphed.

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 $200/hour. Find the most economical speed for a voyage of 1,400 miles.

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 x)(x - 3)² on the interval (1, 5).

Verify that f(x) = x² + 2 satisfies the hypothesis of the Mean-Value Theorem on the interval [0, 4] and find all values of C that satisfy the conclusion of the theorem.

Given y = x^2/3(x + 6). Plot any stationary points, inflections points, and cusps which may or may not exist. Approximate answers to 4 decimal places.

Use a graphing utility to assist in determining the location of the absolute maximum of f(x) = -(x² - 7)² on (- $\infty$ , $\infty$ ), if it exists.

f(x) = |x² - 9| has

Find the relative extreme values for f(x) = 5x³ - 30x² + 7 on the interval [-1, 10] and determine where those values occur.

Answer true or false. All functions of the form f(x) = axⁿ , where n is odd and a $\neq$ 0 have an inflection point.

Given f(x) = -5x³ + 15x² . Use a graphing utility to estimate the absolute maximum and minimum values of f, if any, on the interval [0, 3].

Find all relative extrema of f(x) = x⁴^/⁷.

Find the relative extreme values for f(x) = 3x³ -18x² + 2 on the interval [-1, 10] and determine where those values occur.