Question 1

A divided field is to be constructed with 2720 feet of fence as shown.
For what value of x will the area be a maximum?

Accepted Answer

x = 680 fe

Question 2

Approximate   by applying Newton's Method to the equation x3 -29 = 0. Use 3 for your initial value and calculate five iterations.

Accepted Answer

f(x) = x³ - 29 f '(

Question 3

Answer true or false. Every function has an absolute maximum and an absolute minimum if its domain is restricted to where f is defined on an interval [-a, a], where a is finite and f is continuous on [-a, a].

Accepted Answer

A) True 
 B)False

Question 4

Given   . Find any extrema.

Accepted Answer

Relative m

Question 5

Answer true or false. An object thrown upward reaches a height of s(t) = -9.8t2 + 49t. The object is highest at t = 5, where t is in seconds?

Accepted Answer

A) True 
 B)False

Question 6

Approximate   by applying Newton's Method to the equation x3 - 20 = 0.

Accepted Answer

f(x) = x³ - 20 f '(

Question 7

Answer true or false. f(x) =   has a critical point.

Accepted Answer

A) True 
 B)False

Question 8

Use a graphing utility to estimate the absolute minimum of f(x) = e x (ln x)4 on [1, 5].

Accepted Answer

Question 9

Find the relative extreme values for f(x) = 2x3 - 12x2 + 18x + 12 on the interval [-10, 10] and determine where those values occur.

Accepted Answer

f '(x) = 6x² - 24x + 18 = (3x

Question 10

f(x) = x4 - 8x3 has

Accepted Answer

A)  a relative maximum at x = 6 and no relative minimum. 
B)  no relative maximum and a relative minimum at x = 6. 
C)  a relative maximum at x = 0 and a relative minimum at x = 6. 
D)  a relative maximum at x = 6 and a relative minimum at x = 0. 
E)  a relative maximum at x = 0 and no relative minimum. 
A)  a relative maximum at x = 6 and no relative minimum. 
B)  no relative maximum and a relative minimum at x = 6. 
C)  a relative maximum at x = 0 and a relative minimum at x = 6. 
D)  a relative maximum at x = 6 and a relative minimum at x = 0. 
E)  a relative maximum at x = 0 and no relative minimum.

Question 11

Find s when a = 0.

Accepted Answer

A)  48 
B)  -48 
C)  6 
D)  -6 
E)  0 
A)  48 
B)  -48 
C)  6 
D)  -6 
E)  0

Question 12

Use Newton's Method to find the largest solution of x5 - 5x4 + 4x3-x2 + 2x + 10 = 0.

Accepted Answer

A)  1.8235294 
B)  1.8038147 
C)  1.8035400 
D)  1.8035520 
E)  1.8035532 
A)  1.8235294 
B)  1.8038147 
C)  1.8035400 
D)  1.8035520 
E)  1.8035532

Question 13

s(t) = 5t - 4t3, t$\ge$0. The acceleration function is

Accepted Answer

A)  5 - 8t 
B)  8t 
C)  5 - 8t2 
D)  24t 
E)  5t - 4t 
A)  5 - 8t 
B)  8t 
C)  5 - 8t2 
D)  24t 
E)  5t - 4t

Question 14

Answer true or false. If the graph on the left is a position function, the graph on the right represents the corresponding velocity function.

Accepted Answer

A) True 
 B)False

Question 15

Find the value c such that the conclusion of Rolle's Theorem are satisfied for f(x) = 3x2 - 5 on [-2, 2].

Accepted Answer

A)  0 
B)  -1 
C)  1 
D)  0.5 
E)  -0.5 
A)  0 
B)  -1 
C)  1 
D)  0.5 
E)  -0.5

Question 16

Answer true or false. The rational function   has no vertical asymptote.

Accepted Answer

A) True 
 B)False

A divided field is to be constructed with 2720 feet of fence as shown. For what value of x will the area be a maximum?

Approximate by applying Newton's Method to the equation x³ -29 = 0. Use 3 for your initial value and calculate five iterations.

Answer true or false. Every function has an absolute maximum and an absolute minimum if its domain is restricted to where f is defined on an interval [-a, a], where a is finite and f is continuous on [-a, a].

Given . Find any extrema.

Answer true or false. An object thrown upward reaches a height of s(t) = -9.8t² + 49t. The object is highest at t = 5, where t is in seconds?

Approximate by applying Newton's Method to the equation x³ - 20 = 0.

Answer true or false. f(x) = has a critical point.

Use a graphing utility to estimate the absolute minimum of f(x) = e ^x (ln x)⁴ on [1, 5].

Find the relative extreme values for f(x) = 2x³ - 12x² + 18x + 12 on the interval [-10, 10] and determine where those values occur.

f(x) = x⁴ - 8x³ has

Find s when a = 0.

Use Newton's Method to find the largest solution of x⁵ - 5x⁴ + 4x³-x² + 2x + 10 = 0.

s(t) = 5t - 4t³, t $\ge$ 0. The acceleration function is

Answer true or false. If the graph on the left is a position function, the graph on the right represents the corresponding velocity function.

Find the value c such that the conclusion of Rolle's Theorem are satisfied for f(x) = 3x² - 5 on [-2, 2].

Answer true or false. The rational function has no vertical asymptote.

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

A divided field is to be constructed with 2720 feet of fence as shown. For what value of x will the area be a maximum?

Approximate by applying Newton's Method to the equation x3 -29 = 0. Use 3 for your initial value and calculate five iterations.

Answer true or false. Every function has an absolute maximum and an absolute minimum if its domain is restricted to where f is defined on an interval [-a, a], where a is finite and f is continuous on [-a, a].

Given . Find any extrema.

Answer true or false. An object thrown upward reaches a height of s(t) = -9.8t2 + 49t. The object is highest at t = 5, where t is in seconds?

Approximate by applying Newton's Method to the equation x3 - 20 = 0.

Answer true or false. f(x) = has a critical point.

Use a graphing utility to estimate the absolute minimum of f(x) = e x (ln x)4 on [1, 5].

Find the relative extreme values for f(x) = 2x3 - 12x2 + 18x + 12 on the interval [-10, 10] and determine where those values occur.

f(x) = x4 - 8x3 has

Find s when a = 0.

Use Newton's Method to find the largest solution of x5 - 5x4 + 4x3-x2 + 2x + 10 = 0.

s(t) = 5t - 4t3, t ≥\ge≥ 0. The acceleration function is

Answer true or false. If the graph on the left is a position function, the graph on the right represents the corresponding velocity function.

Find the value c such that the conclusion of Rolle's Theorem are satisfied for f(x) = 3x2 - 5 on [-2, 2].

Answer true or false. The rational function has no vertical asymptote.

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

Approximate by applying Newton's Method to the equation x³ -29 = 0. Use 3 for your initial value and calculate five iterations.

Answer true or false. An object thrown upward reaches a height of s(t) = -9.8t² + 49t. The object is highest at t = 5, where t is in seconds?

Approximate by applying Newton's Method to the equation x³ - 20 = 0.

Use a graphing utility to estimate the absolute minimum of f(x) = e ^x (ln x)⁴ on [1, 5].

Find the relative extreme values for f(x) = 2x³ - 12x² + 18x + 12 on the interval [-10, 10] and determine where those values occur.

f(x) = x⁴ - 8x³ has

Use Newton's Method to find the largest solution of x⁵ - 5x⁴ + 4x³-x² + 2x + 10 = 0.

s(t) = 5t - 4t³, t $\ge$ 0. The acceleration function is

Find the value c such that the conclusion of Rolle's Theorem are satisfied for f(x) = 3x² - 5 on [-2, 2].