Question 1

Express the number 27 as a sum of two nonnegative terms whose product is as large as possible.

Accepted Answer

The answer of Express the number 27 as a sum...

Question 2

Given   . Use a graphing utility to estimate the absolute maximum and minimum values of f, if any, on the interval [-5, 1].

Accepted Answer

Absolute maximum of

Question 3

If f(x) = x5 - 5x + 10. Find the points of inflection.

Accepted Answer

The answer of If f(x) = x5 - 5x +...

Question 4

Given f(x) = 5x3 -2x2- 7x + 9, find the intervals where f is increasing and where f is decreasing.

Accepted Answer

Increasing

Question 5

A poster is to contain 180 in2 of printed matter with margins of 2 in. each at top and bottom and 2 in. at each side. Find the original dimensions of the poster if the total area of the poster with border is to be a minimum.

Accepted Answer

Let the original area be 180 =

Question 6

Find the location of the absolute maximum of 2 tan 5x on [0,  $\pi$], if it exists.

Accepted Answer

A)  2 
B)   $\pi$ 
C)  5 
D)    
E)  None exist. 
A)  2 
B)   $\pi$ 
C)  5 
D)    
E)  None exist.

Question 7

If f(x) = x(x - 3)2 , find the intervals where f is increasing and where f is decreasing.

Accepted Answer

Increasing

Question 8

Suppose that the number of bacteria present in a culture bacteria at time t is given by N = -6000(x2 + 10x - 24). Find the smallest number of bacteria in the culture during the time interval 0 $\le$t $\le$ 1.

Accepted Answer

A)  30,000 
B)  144,000 
C)  294,000 
D)  78,000 
E)  264,000 
A)  30,000 
B)  144,000 
C)  294,000 
D)  78,000 
E)  264,000

Question 9

Use Newton's Method to approximate the solutions of x4 -15 = 0.

Accepted Answer

A)  -1.9679901, 1.9679901 
B)  -1.9679897, 1.9679897 
C)  -1.96875, 1.96875 
D)  -2, 2 
A)  -1.9679901, 1.9679901 
B)  -1.9679897, 1.9679897 
C)  -1.96875, 1.96875 
D)  -2, 2

Question 10

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 = 18 inches? See figure on right.

Accepted Answer

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

Question 11

Find the extreme values for   on the interval [-2, 3] and determine where those values occur.

Accepted Answer

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

Question 12

The position function of a particle is given by s(t) = 3t -2t2 + 4t3. Find the velocity function.

Accepted Answer

v(t) = s'(

Question 13

Find the value of c in the interval [0, 2 $\pi$] that satisfies the Mean Value Theorem. f(x) = 6 cos x

Accepted Answer

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

Question 14

Use a graphing utility to graph f(x) =   . How many points of inflection does the function have?

Accepted Answer

A)  0 
B)  1 
C)  2 
D)  3 
E)  4 
A)  0 
B)  1 
C)  2 
D)  3 
E)  4

Question 15

Approximate   by applying Newton's Method to the equation x2 - 63 = 0.

Accepted Answer

f(x) = x² - 63 f '(

Question 16

Use a graphing utility to estimate the absolute maximum of   on [2, 10].

Accepted Answer

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

Question 17

A long strip of copper 8 inches wide is to be made into a rain gutter by turning up the sides to form a trough with a rectangular cross section. Find the dimensions of the cross section if the carrying capacity of the trough is to be a maximum.

Accepted Answer

The answer of A long strip of copper 8 inches...

Question 18

Find the value for which f(x) = x2 + 2 on [2, 5] satisfies the Mean-Value Theorem.

Accepted Answer

A)  2.5 
B)  3.5 
C)  4.5 
D)  3 
E)  4 
A)  2.5 
B)  3.5 
C)  4.5 
D)  3 
E)  4

Question 19

Answer true or false. f(x) = e7x has a point of inflection.

Accepted Answer

A) True 
 B)False

Question 20

s(t) = t5 -10, t   0. Find s when a = 0.

Accepted Answer

A)   20 
B)   -20 
C)   10 
D)   -10 
E)   0 
A)   20 
B)   -20 
C)   10 
D)   -10 
E)   0

Express the number 27 as a sum of two nonnegative terms whose product is as large as possible.

Given . Use a graphing utility to estimate the absolute maximum and minimum values of f, if any, on the interval [-5, 1].

If f(x) = x⁵ - 5x + 10. Find the points of inflection.

Given f(x) = 5x³ -2x²- 7x + 9, find the intervals where f is increasing and where f is decreasing.

A poster is to contain 180 in² of printed matter with margins of 2 in. each at top and bottom and 2 in. at each side. Find the original dimensions of the poster if the total area of the poster with border is to be a minimum.

Find the location of the absolute maximum of 2 tan 5x on [0, $\pi$ ], if it exists.

If f(x) = x(x - 3)² , find the intervals where f is increasing and where f is decreasing.

Suppose that the number of bacteria present in a culture bacteria at time t is given by N = -6000(x² + 10x - 24). Find the smallest number of bacteria in the culture during the time interval 0 $\le$ t $\le$ 1.

Use Newton's Method to approximate the solutions of x⁴ -15 = 0.

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 = 18 inches? See figure on right.

Find the extreme values for on the interval [-2, 3] and determine where those values occur.

The position function of a particle is given by s(t) = 3t -2t² + 4t³. Find the velocity function.

Find the value of c in the interval [0, 2 $\pi$ ] that satisfies the Mean Value Theorem. f(x) = 6 cos x

Use a graphing utility to graph f(x) = . How many points of inflection does the function have?

Approximate by applying Newton's Method to the equation x² - 63 = 0.

Use a graphing utility to estimate the absolute maximum of on [2, 10].

A long strip of copper 8 inches wide is to be made into a rain gutter by turning up the sides to form a trough with a rectangular cross section. Find the dimensions of the cross section if the carrying capacity of the trough is to be a maximum.

Find the value for which f(x) = x² + 2 on [2, 5] satisfies the Mean-Value Theorem.

Answer true or false. f(x) = e⁷^x has a point of inflection.

s(t) = t⁵ -10, t 0. Find s 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

Express the number 27 as a sum of two nonnegative terms whose product is as large as possible.

Given . Use a graphing utility to estimate the absolute maximum and minimum values of f, if any, on the interval [-5, 1].

If f(x) = x5 - 5x + 10. Find the points of inflection.

Given f(x) = 5x3 -2x2- 7x + 9, find the intervals where f is increasing and where f is decreasing.

A poster is to contain 180 in2 of printed matter with margins of 2 in. each at top and bottom and 2 in. at each side. Find the original dimensions of the poster if the total area of the poster with border is to be a minimum.

Find the location of the absolute maximum of 2 tan 5x on [0, π\piπ ], if it exists.

If f(x) = x(x - 3)2 , find the intervals where f is increasing and where f is decreasing.

Suppose that the number of bacteria present in a culture bacteria at time t is given by N = -6000(x2 + 10x - 24). Find the smallest number of bacteria in the culture during the time interval 0 ≤\le≤ t ≤\le≤ 1.

Use Newton's Method to approximate the solutions of x4 -15 = 0.

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 = 18 inches? See figure on right.

Find the extreme values for on the interval [-2, 3] and determine where those values occur.

The position function of a particle is given by s(t) = 3t -2t2 + 4t3. Find the velocity function.

Find the value of c in the interval [0, 2 π\piπ ] that satisfies the Mean Value Theorem. f(x) = 6 cos x

Use a graphing utility to graph f(x) = . How many points of inflection does the function have?

Approximate by applying Newton's Method to the equation x2 - 63 = 0.

Use a graphing utility to estimate the absolute maximum of on [2, 10].

A long strip of copper 8 inches wide is to be made into a rain gutter by turning up the sides to form a trough with a rectangular cross section. Find the dimensions of the cross section if the carrying capacity of the trough is to be a maximum.

Find the value for which f(x) = x2 + 2 on [2, 5] satisfies the Mean-Value Theorem.

Answer true or false. f(x) = e7x has a point of inflection.

s(t) = t5 -10, t 0. Find s 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

If f(x) = x⁵ - 5x + 10. Find the points of inflection.

Given f(x) = 5x³ -2x²- 7x + 9, find the intervals where f is increasing and where f is decreasing.

A poster is to contain 180 in² of printed matter with margins of 2 in. each at top and bottom and 2 in. at each side. Find the original dimensions of the poster if the total area of the poster with border is to be a minimum.

Find the location of the absolute maximum of 2 tan 5x on [0, $\pi$ ], if it exists.

If f(x) = x(x - 3)² , find the intervals where f is increasing and where f is decreasing.

Suppose that the number of bacteria present in a culture bacteria at time t is given by N = -6000(x² + 10x - 24). Find the smallest number of bacteria in the culture during the time interval 0 $\le$ t $\le$ 1.

Use Newton's Method to approximate the solutions of x⁴ -15 = 0.

The position function of a particle is given by s(t) = 3t -2t² + 4t³. Find the velocity function.

Find the value of c in the interval [0, 2 $\pi$ ] that satisfies the Mean Value Theorem. f(x) = 6 cos x

Approximate by applying Newton's Method to the equation x² - 63 = 0.

Find the value for which f(x) = x² + 2 on [2, 5] satisfies the Mean-Value Theorem.

Answer true or false. f(x) = e⁷^x has a point of inflection.

s(t) = t⁵ -10, t 0. Find s when a = 0.