Question 1

Find the relative extrema for f(x) = x4 -12x2 + 7.

Accepted Answer

f '(x) = 4x(x² - 6) Critical

Question 2

The equation,   has one real solution for   . Approximate it by Newton's Method. Use 2 for your initial value and calculate eight iterations.

Accepted Answer

@#IMG-DLM& @#IMG-DLM& @#IMG-DLM& x₁ = 2 x₂ = 2.323732 x₃ = 2.27

Question 3

The position function of a particle is given by s(t) = t4. Find the acceleration function.

Accepted Answer

Question 4

Use Newton's Method to find the largest positive solution of x3 + x2 - 2x - 5 = 3.

Accepted Answer

A)  2.9629630 
B)  2.3677783 
C)  2.0980398 
D)  2.0000079 
E)  2.0178463 
A)  2.9629630 
B)  2.3677783 
C)  2.0980398 
D)  2.0000079 
E)  2.0178463

Question 5

Find the value for which f(x) = x2 + 5 on [1, 5] satisfies the Mean-Value Theorem.

Accepted Answer

A)  1.5 
B)  3 
C)  4.5 
D)  2.33 
E)  3.66 
A)  1.5 
B)  3 
C)  4.5 
D)  2.33 
E)  3.66

Question 6

The absolute minimum of   occurs at x =

Accepted Answer

A)  0 
B)  4 
C)  2 
D)  -2 
E)  None exists 
A)  0 
B)  4 
C)  2 
D)  -2 
E)  None exists

Question 7

A long strip of copper W = 24 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 W =...

Question 8

If f(x) = sin 6x (0,  $\pi$/3), find the inflection points.

Accepted Answer

The answer of If f(x) = sin 6x (0, ...

Question 9

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 10

The graph represents a velocity function. The acceleration at t = 2 is

Accepted Answer

A)  negative 
B)  positive 
C)  zero 
D)  There is insufficient information to tell. 
E)  It is +$\infty$ 
A)  negative 
B)  positive 
C)  zero 
D)  There is insufficient information to tell. 
E)  It is +$\infty$

Question 11

Two numbers sum to 168. Find the two numbers whose product is maximum.

Accepted Answer

A)  28, 162 
B)  7, 161 
C)  24, 164 
D)  84, 84 
E)  42, 126 
A)  28, 162 
B)  7, 161 
C)  24, 164 
D)  84, 84 
E)  42, 126

Question 12

Answer true or false. f(x) = e3x has a horizontal asymptote at y = 0.

Accepted Answer

A) True 
 B)False

Question 13

Find the point on the curve x2 + y2 = 144 closest to (0, 16).

Accepted Answer

A)  (0, 144) 
B)  (0, 12) 
C)  (0, 16) 
D)  (12, 0) 
E)  (144, 0) 
A)  (0, 144) 
B)  (0, 12) 
C)  (0, 16) 
D)  (12, 0) 
E)  (144, 0)

Question 14

Answer true or false. The point on the parabola y = 5x2 closest to (0, 0.8) is (0, 0).

Accepted Answer

A) True 
 B)False

Question 15

f(x) = x2 -6x -16 has an absolute minimum on [-5, 5] of

Accepted Answer

A)  -25 
B)  7 
C)  3 
D)  11 
E)  -31 
A)  -25 
B)  7 
C)  3 
D)  11 
E)  -31

Question 16

Find the extreme values for   on the interval [-2, 4] and determine where those values occur.

Accepted Answer

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

Question 17

Does   satisfy the hypothesis of the Mean-Value Theorem over the interval [0, 16]? If so, find all values of C that satisfy the conclusion of the theorem.

Accepted Answer

Yes, since f is continuous ove

Question 18

Answer true or false. f(x) = 7xe 3x has a relative minimum.

Accepted Answer

A) True 
 B)False

Question 19

f(x) = cos(3x) has an absolute minimum on [0,  $\pi$] at x =

Accepted Answer

A)   $\pi$ 
B)    
C)  3 
D)  2 $\pi$ 
E)  None exist 
A)   $\pi$ 
B)    
C)  3 
D)  2 $\pi$ 
E)  None exist

Question 20

f(x) = 4x2 - 4x + 6 on (-$\infty$, $\infty$) has

Accepted Answer

A)  only an absolute maximum 
B)  only an absolute minimum 
C)  both an absolute maximum and an absolute minimum 
D)  neither an absolute maximum nor an absolute minimum. 
E)  cannot be determined 
A)  only an absolute maximum 
B)  only an absolute minimum 
C)  both an absolute maximum and an absolute minimum 
D)  neither an absolute maximum nor an absolute minimum. 
E)  cannot be determined

Find the relative extrema for f(x) = x⁴ -12x² + 7.

The equation, has one real solution for . Approximate it by Newton's Method. Use 2 for your initial value and calculate eight iterations.

The position function of a particle is given by s(t) = t⁴. Find the acceleration function.

Use Newton's Method to find the largest positive solution of x³ + x² - 2x - 5 = 3.

Find the value for which f(x) = x² + 5 on [1, 5] satisfies the Mean-Value Theorem.

The absolute minimum of occurs at x =

A long strip of copper W = 24 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.

If f(x) = sin 6x (0, $\pi$ /3), find the inflection points.

f(x) = |x² -9| has

The graph represents a velocity function. The acceleration at t = 2 is

Two numbers sum to 168. Find the two numbers whose product is maximum.

Answer true or false. f(x) = e³^x has a horizontal asymptote at y = 0.

Find the point on the curve x² + y² = 144 closest to (0, 16).

Answer true or false. The point on the parabola y = 5x² closest to (0, 0.8) is (0, 0).

f(x) = x² -6x -16 has an absolute minimum on [-5, 5] of

Find the extreme values for on the interval [-2, 4] and determine where those values occur.

Does satisfy the hypothesis of the Mean-Value Theorem over the interval [0, 16]? If so, find all values of C that satisfy the conclusion of the theorem.

Answer true or false. f(x) = 7xe ³^x has a relative minimum.

f(x) = cos(3x) has an absolute minimum on [0, $\pi$ ] at x =

f(x) = 4x² - 4x + 6 on (- $\infty$ , $\infty$ ) has

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 extrema for f(x) = x4 -12x2 + 7.

The equation, has one real solution for . Approximate it by Newton's Method. Use 2 for your initial value and calculate eight iterations.

The position function of a particle is given by s(t) = t4. Find the acceleration function.

Use Newton's Method to find the largest positive solution of x3 + x2 - 2x - 5 = 3.

Find the value for which f(x) = x2 + 5 on [1, 5] satisfies the Mean-Value Theorem.

The absolute minimum of occurs at x =

A long strip of copper W = 24 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.

If f(x) = sin 6x (0, π\piπ /3), find the inflection points.

f(x) = |x2 -9| has

The graph represents a velocity function. The acceleration at t = 2 is

Two numbers sum to 168. Find the two numbers whose product is maximum.

Answer true or false. f(x) = e3x has a horizontal asymptote at y = 0.

Find the point on the curve x2 + y2 = 144 closest to (0, 16).

Answer true or false. The point on the parabola y = 5x2 closest to (0, 0.8) is (0, 0).

f(x) = x2 -6x -16 has an absolute minimum on [-5, 5] of

Find the extreme values for on the interval [-2, 4] and determine where those values occur.

Does satisfy the hypothesis of the Mean-Value Theorem over the interval [0, 16]? If so, find all values of C that satisfy the conclusion of the theorem.

Answer true or false. f(x) = 7xe 3x has a relative minimum.

f(x) = cos(3x) has an absolute minimum on [0, π\piπ ] at x =

f(x) = 4x2 - 4x + 6 on (- ∞\infty∞ , ∞\infty∞ ) has

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

Find the relative extrema for f(x) = x⁴ -12x² + 7.

The position function of a particle is given by s(t) = t⁴. Find the acceleration function.

Use Newton's Method to find the largest positive solution of x³ + x² - 2x - 5 = 3.

Find the value for which f(x) = x² + 5 on [1, 5] satisfies the Mean-Value Theorem.

If f(x) = sin 6x (0, $\pi$ /3), find the inflection points.

f(x) = |x² -9| has

Answer true or false. f(x) = e³^x has a horizontal asymptote at y = 0.

Find the point on the curve x² + y² = 144 closest to (0, 16).

Answer true or false. The point on the parabola y = 5x² closest to (0, 0.8) is (0, 0).

f(x) = x² -6x -16 has an absolute minimum on [-5, 5] of

Answer true or false. f(x) = 7xe ³^x has a relative minimum.

f(x) = cos(3x) has an absolute minimum on [0, $\pi$ ] at x =

f(x) = 4x² - 4x + 6 on (- $\infty$ , $\infty$ ) has