Question 1

Find the value of c in the interval [0, 2] that satisfies the Mean Value Theorem. f(x) = 3x2 + 12

Accepted Answer

@#IMG-DLM& 6
f '(x)

Question 2

f(x) = cos21.45x on 0 < x < 2 $\pi$ has

Accepted Answer

A)  a relative maximum only 
B)  a relative minimum only 
C)  both a relative maximum and a relative minimum 
D)  neither a relative maximum nor a relative minimum 
E)  cannot be determined 
A)  a relative maximum only 
B)  a relative minimum only 
C)  both a relative maximum and a relative minimum 
D)  neither a relative maximum nor a relative minimum 
E)  cannot be determined

Question 3

A projectile is dropped, and reaches the ground at 40 m/s. How long does it take the projectile to reach ground? (Assume the position function is   , where a = -10   .)

Accepted Answer

A)  2 s 
B)  8 s 
C)  4.47 s 
D)  4 s 
E)  3.16 s 
A)  2 s 
B)  8 s 
C)  4.47 s 
D)  4 s 
E)  3.16 s

Question 4

The rational function   has

Accepted Answer

A)  a horizontal asymptote at y = 1 
B)  a horizontal asymptote at y = 10 
C)  a horizontal asymptote at y = -1 
D)  a horizontal asymptote at y = 0 
E)  no horizontal asymptote 
A)  a horizontal asymptote at y = 1 
B)  a horizontal asymptote at y = 10 
C)  a horizontal asymptote at y = -1 
D)  a horizontal asymptote at y = 0 
E)  no horizontal asymptote

Question 5

Use Newton's Method to approximate the greatest x-coordinate of the intersection of y = x3 - 2x and y = x4 + 6x - 4. Use 3 for your initial value and calculate eight iterations.

Accepted Answer

A)  0.5169625 
B)  0.7963536 
C)  0.5080644 
D)  1.4400943 
E)  2.1685393 
A)  0.5169625 
B)  0.7963536 
C)  0.5080644 
D)  1.4400943 
E)  2.1685393

Question 6

f(x) = 5x2- 30x-35 has an absolute minimum on [-5, 5] of

Accepted Answer

A)  -80 
B)  -10 
C)  3 
D)  100 
E)  -110 
A)  -80 
B)  -10 
C)  3 
D)  100 
E)  -110

Question 7

Find the point on the parabola 2y = x2 which is closest to (12, 17).

Accepted Answer

=Since @#IMG-DLM& let @#IMG-DLM& be the distance from (12, 1

Question 8

Sketch the graph of y = 3 + (x -5)1/3. Find any critical points and any inflections points.

Accepted Answer

@#IMG-DLM& @#IMG-DLM& Critical point at

Question 9

Given f(x) = -2x5 + 20x4 . Use a graphing utility to estimate the absolute maximum and minimum values of f, if any, on the interval [0, 10].

Accepted Answer

Absolute maximum of

Question 10

Find the extreme values for f(x) = 4x4/3 -6x1/3 on the interval [-1, 8] and determine where those values occur.

Accepted Answer

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

Question 11

Does   satisfy the hypothesis of the Mean-Value Theorem over the interval [-5, 5]? If so, find all values of C that satisfy the conclusion.

Accepted Answer

No, since f is not d

Question 12

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

Accepted Answer

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

Question 13

The rational function   has

Accepted Answer

A)  a stationary point at x = 1 
B)  a stationary point at x = -1 
C)  two stationary points at approximately x = -1.495 and x = 1.495 
D)  three stationary points approximately at x = 0, x = -1.495 and x = 1.495 
E)  no stationary points 
A)  a stationary point at x = 1 
B)  a stationary point at x = -1 
C)  two stationary points at approximately x = -1.495 and x = 1.495 
D)  three stationary points approximately at x = 0, x = -1.495 and x = 1.495 
E)  no stationary points

Question 14

The position function of a particle is given by s = 6t3 - 3t2 + 9t + 6 for t $\ge$ 0. Find the functions for v and a.

Accepted Answer

v = 18t<su

Question 15

If f(x) = x(x- 9)2 , find the intervals where f is increasing and where f is decreasing.

Accepted Answer

Increasing

Question 16

Answer true or false. If a particle is dropped a distance of 624 m. It has a speed of 110.58 m/s (rounded to the nearest hundredth of a m/s) when it hits the ground.

Accepted Answer

A) True 
 B)False

Question 17

Answer true or false. f(x) = x3 -11x2 + 120x + 13 restricted to a domain of [0, 20] has an absolute maximum at x = 4 of 381, and an absolute minimum at x = 10 of 1,113.

Accepted Answer

A) True 
 B)False

Question 18

Use Rolle's Theorem to show that f(x) = x3 + ax + b, where a > 0, cannot have more than one real root.

Accepted Answer

Suppose f has more than one real root. L

Question 19

Answer true or false. If f(x) has an absolute minimum at x = 6, -f(x) also has an absolute minimum at x = 6.

Accepted Answer

A) True 
 B)False

Question 20

Find the extreme values for   on the interval [0, 17] and determine where those values occur.

Accepted Answer

@#IMG-DLM& ; f '(x) = 0 when x = -16 and

Find the value of c in the interval [0, 2] that satisfies the Mean Value Theorem. f(x) = 3x² + 12

f(x) = cos²1.45x on 0 < x < 2 $\pi$ has

A projectile is dropped, and reaches the ground at 40 m/s. How long does it take the projectile to reach ground? (Assume the position function is , where a = -10 .)

The rational function has

Use Newton's Method to approximate the greatest x-coordinate of the intersection of y = x³ - 2x and y = x⁴ + 6x - 4. Use 3 for your initial value and calculate eight iterations.

f(x) = 5x²- 30x-35 has an absolute minimum on [-5, 5] of

Find the point on the parabola 2y = x² which is closest to (12, 17).

Sketch the graph of y = 3 + (x -5)^1/3. Find any critical points and any inflections points.

Given f(x) = -2x⁵ + 20x⁴ . Use a graphing utility to estimate the absolute maximum and minimum values of f, if any, on the interval [0, 10].

Find the extreme values for f(x) = 4x^4/3 -6x^1/3 on the interval [-1, 8] and determine where those values occur.

Does satisfy the hypothesis of the Mean-Value Theorem over the interval [-5, 5]? If so, find all values of C that satisfy the conclusion.

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

The rational function has

The position function of a particle is given by s = 6t³ - 3t² + 9t + 6 for t $\ge$ 0. Find the functions for v and a.

If f(x) = x(x- 9)² , find the intervals where f is increasing and where f is decreasing.

Answer true or false. If a particle is dropped a distance of 624 m. It has a speed of 110.58 m/s (rounded to the nearest hundredth of a m/s) when it hits the ground.

Answer true or false. f(x) = x³ -11x² + 120x + 13 restricted to a domain of [0, 20] has an absolute maximum at x = 4 of 381, and an absolute minimum at x = 10 of 1,113.

Use Rolle's Theorem to show that f(x) = x³ + ax + b, where a > 0, cannot have more than one real root.

Answer true or false. If f(x) has an absolute minimum at x = 6, -f(x) also has an absolute minimum at x = 6.

Find the extreme values for on the interval [0, 17] and determine where those values occur.

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 value of c in the interval [0, 2] that satisfies the Mean Value Theorem. f(x) = 3x2 + 12

f(x) = cos21.45x on 0 < x < 2 π\piπ has

A projectile is dropped, and reaches the ground at 40 m/s. How long does it take the projectile to reach ground? (Assume the position function is , where a = -10 .)

The rational function has

Use Newton's Method to approximate the greatest x-coordinate of the intersection of y = x3 - 2x and y = x4 + 6x - 4. Use 3 for your initial value and calculate eight iterations.

f(x) = 5x2- 30x-35 has an absolute minimum on [-5, 5] of

Find the point on the parabola 2y = x2 which is closest to (12, 17).

Sketch the graph of y = 3 + (x -5)1/3. Find any critical points and any inflections points.

Given f(x) = -2x5 + 20x4 . Use a graphing utility to estimate the absolute maximum and minimum values of f, if any, on the interval [0, 10].

Find the extreme values for f(x) = 4x4/3 -6x1/3 on the interval [-1, 8] and determine where those values occur.

Does satisfy the hypothesis of the Mean-Value Theorem over the interval [-5, 5]? If so, find all values of C that satisfy the conclusion.

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

The rational function has

The position function of a particle is given by s = 6t3 - 3t2 + 9t + 6 for t ≥\ge≥ 0. Find the functions for v and a.

If f(x) = x(x- 9)2 , find the intervals where f is increasing and where f is decreasing.

Answer true or false. If a particle is dropped a distance of 624 m. It has a speed of 110.58 m/s (rounded to the nearest hundredth of a m/s) when it hits the ground.

Answer true or false. f(x) = x3 -11x2 + 120x + 13 restricted to a domain of [0, 20] has an absolute maximum at x = 4 of 381, and an absolute minimum at x = 10 of 1,113.

Use Rolle's Theorem to show that f(x) = x3 + ax + b, where a > 0, cannot have more than one real root.

Answer true or false. If f(x) has an absolute minimum at x = 6, -f(x) also has an absolute minimum at x = 6.

Find the extreme values for on the interval [0, 17] and determine where those values occur.

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 value of c in the interval [0, 2] that satisfies the Mean Value Theorem. f(x) = 3x² + 12

f(x) = cos²1.45x on 0 < x < 2 $\pi$ has

Use Newton's Method to approximate the greatest x-coordinate of the intersection of y = x³ - 2x and y = x⁴ + 6x - 4. Use 3 for your initial value and calculate eight iterations.

f(x) = 5x²- 30x-35 has an absolute minimum on [-5, 5] of

Find the point on the parabola 2y = x² which is closest to (12, 17).

Sketch the graph of y = 3 + (x -5)^1/3. Find any critical points and any inflections points.

Given f(x) = -2x⁵ + 20x⁴ . Use a graphing utility to estimate the absolute maximum and minimum values of f, if any, on the interval [0, 10].

Find the extreme values for f(x) = 4x^4/3 -6x^1/3 on the interval [-1, 8] and determine where those values occur.

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

The position function of a particle is given by s = 6t³ - 3t² + 9t + 6 for t $\ge$ 0. Find the functions for v and a.

If f(x) = x(x- 9)² , find the intervals where f is increasing and where f is decreasing.

Answer true or false. f(x) = x³ -11x² + 120x + 13 restricted to a domain of [0, 20] has an absolute maximum at x = 4 of 381, and an absolute minimum at x = 10 of 1,113.

Use Rolle's Theorem to show that f(x) = x³ + ax + b, where a > 0, cannot have more than one real root.