Question 1

Use Newton's Method to find the largest positive solution of x4 - 3x2 - 9 = 0. Use 5 for your initial value and calculate eight iterations.

Accepted Answer

A)  2.2697369 
B)  2.5222928 
C)  2.2032027 
D)  3.0390141 
E)  3.8489362 
A)  2.2697369 
B)  2.5222928 
C)  2.2032027 
D)  3.0390141 
E)  3.8489362

Question 2

The largest open interval over which f is concave up for   is

Accepted Answer

A)  (4, $\infty$) 
B)  (-$\infty$, 4) 
C)  (-$\infty$, $\infty$) 
D)  (-4, 4) 
E)  nowhere 
A)  (4, $\infty$) 
B)  (-$\infty$, 4) 
C)  (-$\infty$, $\infty$) 
D)  (-4, 4) 
E)  nowhere

Question 3

Express the number 42 as a sum of two nonnegative terms whose product is as large as possible.

Accepted Answer

The answer of Express the number 42 as a sum...

Question 4

Use Newton's Method to approximate the solutions of x4- 77 = 0. Use 4 for your initial value and calculate four iterations.

Accepted Answer

A)  -3.0108653, 3.0108653 
B)  -2.9634212, 2.9634212 
C)  -2.9622573, 2.9622573 
D)  -3.300781, 3.300781 
E)  -4, 4 
A)  -3.0108653, 3.0108653 
B)  -2.9634212, 2.9634212 
C)  -2.9622573, 2.9622573 
D)  -3.300781, 3.300781 
E)  -4, 4

Question 5

Find all relative extrema of f(x) = (x + 1)3.

Accepted Answer

Question 6

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 7

Find all relative extrema of f(x) = (x + 5)2 -11.

Accepted Answer

Relative m

Question 8

Given   . Find any extrema and points of inflection.

Accepted Answer

@#IMG-DLM& @#IMG-DLM& Inflection points

Question 9

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

Accepted Answer

@#IMG-DLM& @#IMG-DLM& Relative minimum a

Question 10

An automobile starts from rest and travels 4.5 miles along a straight road in 6 minutes. Use the Mean-Value Theorem to show that at some instant during the trip its velocity was exactly 45 miles per hour.

Accepted Answer

Let s = f(t) be the position versus time

Question 11

A line is drawn through the point P(3, 6) so that it intersects the y-axis at A(0, y) and the x-axis at B(x,0). Find the smallest triangle formed if x and y are positive.

Accepted Answer

@#IMG-DLM& . The slope of the line throu

Question 12

Express the number 56 as the sum of two nonnegative numbers whose product is as large as possible.

Accepted Answer

A)  0, 56 
B)  41, 15 
C)  28, 28 
D)  40, 16 
E)  31, 25 
A)  0, 56 
B)  41, 15 
C)  28, 28 
D)  40, 16 
E)  31, 25

Question 13

A storm is passing with the wind speed in mph changing over time according to v(t) = -t2 + 22t -40, for 0 $\le$ t $\le$ 11. Find the highest wind speed that occurs.

Accepted Answer

A)  323 mph 
B)  161 mph 
C)  403 mph 
D)  59 mph 
E)  81 mph 
A)  323 mph 
B)  161 mph 
C)  403 mph 
D)  59 mph 
E)  81 mph

Question 14

Find all relative extrema of   .

Accepted Answer

The answer of Find all relative extrema of  ...

Question 15

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

Accepted Answer

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

Question 16

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 17

Use a graphing utility to estimate the absolute maximum of f(x) = -e2x on [-3, 3]. at

Accepted Answer

Question 18

Answer true or false. A graphing utility can be used to show f(x) = |x6| has a relative maximum.

Accepted Answer

A) True 
 B)False

Question 19

f(x) = x4 - 3x2 - 9 is concave down on the interval I = (Approximate your answer to 3 decimal places.)

Accepted Answer

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

Question 20

Find the point on the curve x2 + y2 = 16 closest to (7, 0).

Accepted Answer

Use Newton's Method to find the largest positive solution of x⁴ - 3x² - 9 = 0. Use 5 for your initial value and calculate eight iterations.

The largest open interval over which f is concave up for is

Express the number 42 as a sum of two nonnegative terms whose product is as large as possible.

Use Newton's Method to approximate the solutions of x⁴- 77 = 0. Use 4 for your initial value and calculate four iterations.

Find all relative extrema of f(x) = (x + 1)³.

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.]

Find all relative extrema of f(x) = (x + 5)² -11.

Given . Find any extrema and points of inflection.

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

An automobile starts from rest and travels 4.5 miles along a straight road in 6 minutes. Use the Mean-Value Theorem to show that at some instant during the trip its velocity was exactly 45 miles per hour.

A line is drawn through the point P(3, 6) so that it intersects the y-axis at A(0, y) and the x-axis at B(x,0). Find the smallest triangle formed if x and y are positive.

Express the number 56 as the sum of two nonnegative numbers whose product is as large as possible.

A storm is passing with the wind speed in mph changing over time according to v(t) = -t² + 22t -40, for 0 $\le$ t $\le$ 11. Find the highest wind speed that occurs.

Find all relative extrema of .

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

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

Use a graphing utility to estimate the absolute maximum of f(x) = -e²^x on [-3, 3]. at

Answer true or false. A graphing utility can be used to show f(x) = |x⁶| has a relative maximum.

f(x) = x⁴ - 3x² - 9 is concave down on the interval I = (Approximate your answer to 3 decimal places.)

Find the point on the curve x² + y² = 16 closest to (7, 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

Use Newton's Method to find the largest positive solution of x4 - 3x2 - 9 = 0. Use 5 for your initial value and calculate eight iterations.

The largest open interval over which f is concave up for is

Express the number 42 as a sum of two nonnegative terms whose product is as large as possible.

Use Newton's Method to approximate the solutions of x4- 77 = 0. Use 4 for your initial value and calculate four iterations.

Find all relative extrema of f(x) = (x + 1)3.

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.]

Find all relative extrema of f(x) = (x + 5)2 -11.

Given . Find any extrema and points of inflection.

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

An automobile starts from rest and travels 4.5 miles along a straight road in 6 minutes. Use the Mean-Value Theorem to show that at some instant during the trip its velocity was exactly 45 miles per hour.

A line is drawn through the point P(3, 6) so that it intersects the y-axis at A(0, y) and the x-axis at B(x,0). Find the smallest triangle formed if x and y are positive.

Express the number 56 as the sum of two nonnegative numbers whose product is as large as possible.

A storm is passing with the wind speed in mph changing over time according to v(t) = -t2 + 22t -40, for 0 ≤\le≤ t ≤\le≤ 11. Find the highest wind speed that occurs.

Find all relative extrema of .

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

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

Use a graphing utility to estimate the absolute maximum of f(x) = -e2x on [-3, 3]. at

Answer true or false. A graphing utility can be used to show f(x) = |x6| has a relative maximum.

f(x) = x4 - 3x2 - 9 is concave down on the interval I = (Approximate your answer to 3 decimal places.)

Find the point on the curve x2 + y2 = 16 closest to (7, 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

Use Newton's Method to find the largest positive solution of x⁴ - 3x² - 9 = 0. Use 5 for your initial value and calculate eight iterations.

Use Newton's Method to approximate the solutions of x⁴- 77 = 0. Use 4 for your initial value and calculate four iterations.

Find all relative extrema of f(x) = (x + 1)³.

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.]

Find all relative extrema of f(x) = (x + 5)² -11.

A storm is passing with the wind speed in mph changing over time according to v(t) = -t² + 22t -40, for 0 $\le$ t $\le$ 11. Find the highest wind speed that occurs.

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

Use a graphing utility to estimate the absolute maximum of f(x) = -e²^x on [-3, 3]. at

Answer true or false. A graphing utility can be used to show f(x) = |x⁶| has a relative maximum.

f(x) = x⁴ - 3x² - 9 is concave down on the interval I = (Approximate your answer to 3 decimal places.)

Find the point on the curve x² + y² = 16 closest to (7, 0).