Question 1

The largest interval over which f is increasing for   is

Accepted Answer

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

Question 2

Find the value of c in the interval [0, 4] that satisfies the Mean Value Theorem. f(x) = 5x2 + 20

Accepted Answer

@#IMG-DLM& 20
f '(x)

Question 3

Given the position function s = 2t3 - 12t2 ; find s and v when a = 0 (Where v is the velocity and a is the acceleration.).

Accepted Answer

v = 6t² - 24t a = 1

Question 4

Use Rolle's Theorem to show that f(x) = 2x3 + 2x - 6 does not have more than one real root.

Accepted Answer

Suppose f has more than one real root. L

Question 5

Given f(x) = -x5 + 15x4 . Use a graphing utility to estimate the absolute maximum and minimum values of f, if any, on the interval [0, 15].

Accepted Answer

Absolute maximum of

Question 6

If f(x) = x4 . Use a graphing utility to estimate the absolute maximum and minimum values of f, if any, on the interval [-1, 2].

Accepted Answer

Absolute minimum of

Question 7

Find the relative extrema for f(x) = 8x - sin 2x, 0 < x <  $\pi$.

Accepted Answer

f '(x) = 8 - 2 cos 2x
Critical

Question 8

Given f(x) = -2x5 + 20x2 . Use a graphing utility to estimate the absolute maximum and minimum values of f, if any, on the interval [0, 3].

Accepted Answer

Absolute minimum of

Question 9

Find the relative extrema for   .

Accepted Answer

Relative m

Question 10

Verify that f(x) = x3 - x satisfies the hypothesis of Rolle's Theorem on the interval [-1, 1] and find all values of C in (-1, 1) such that f '(C) = 0

Accepted Answer

f(-1) = f(1) = 0
f '

Question 11

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

Accepted Answer

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

Question 12

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 maximum a

Question 13

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

Accepted Answer

Increasing

Question 14

Use Rolle's Theorem to prove that the equation 8x7 - 16x3 + 3 = 0 has at least one solution in the interval (0, 1).

Accepted Answer

If f(x) = x⁸ - 4x

Question 15

Find the value of c in the interval [0,  $\pi$] that satisfies the Mean Value Theorem. f(x) = sin(8x)

Accepted Answer

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

Question 16

Use a graphing utility to estimate the absolute minimum of f(x) = x4e x on [-1, 1].

Accepted Answer

Question 17

Find the dimensions of the rectangle of maximum area which may be embedded in a right triangle with base of 5, height of 12, and hypotenuse of 13 feet as shown in the figure.

Accepted Answer

The answer of Find the dimensions of the rectangle of...

Question 18

The function   has

Accepted Answer

A)  points of inflection at x = -36 and x = 36 
B)  points of inflection at x = -6 and x = 6 
C)  points of inflection at x = 0 
D)  no point of inflection 
E)  points of inflection at x = 6 
A)  points of inflection at x = -36 and x = 36 
B)  points of inflection at x = -6 and x = 6 
C)  points of inflection at x = 0 
D)  no point of inflection 
E)  points of inflection at x = 6

Question 19

If f(x) = 4x4 - 9x3 , find the intervals where f is concave up and where f is concave down.

Accepted Answer

Concave up

Question 20

If f(x) = 6x4 - 24x3 + 5 , find the intervals where f is increasing and where f is decreasing.

Accepted Answer

Increasing

The largest interval over which f is increasing for is

Find the value of c in the interval [0, 4] that satisfies the Mean Value Theorem. f(x) = 5x² + 20

Given the position function s = 2t³ - 12t² ; find s and v when a = 0 (Where v is the velocity and a is the acceleration.).

Use Rolle's Theorem to show that f(x) = 2x³ + 2x - 6 does not have more than one real root.

Given f(x) = -x⁵ + 15x⁴ . Use a graphing utility to estimate the absolute maximum and minimum values of f, if any, on the interval [0, 15].

If f(x) = x⁴ . Use a graphing utility to estimate the absolute maximum and minimum values of f, if any, on the interval [-1, 2].

Find the relative extrema for f(x) = 8x - sin 2x, 0 < x < $\pi$ .

Given f(x) = -2x⁵ + 20x² . Use a graphing utility to estimate the absolute maximum and minimum values of f, if any, on the interval [0, 3].

Find the relative extrema for .

Verify that f(x) = x³ - x satisfies the hypothesis of Rolle's Theorem on the interval [-1, 1] and find all values of C in (-1, 1) such that f '(C) = 0

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

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

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

Use Rolle's Theorem to prove that the equation 8x⁷ - 16x³ + 3 = 0 has at least one solution in the interval (0, 1).

Find the value of c in the interval [0, $\pi$ ] that satisfies the Mean Value Theorem. f(x) = sin(8x)

Use a graphing utility to estimate the absolute minimum of f(x) = x⁴e ^x on [-1, 1].

Find the dimensions of the rectangle of maximum area which may be embedded in a right triangle with base of 5, height of 12, and hypotenuse of 13 feet as shown in the figure.

The function has

If f(x) = 4x⁴ - 9x³ , find the intervals where f is concave up and where f is concave down.

If f(x) = 6x⁴ - 24x³ + 5 , find the intervals where f is increasing and where f is decreasing.

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

The largest interval over which f is increasing for is

Find the value of c in the interval [0, 4] that satisfies the Mean Value Theorem. f(x) = 5x2 + 20

Given the position function s = 2t3 - 12t2 ; find s and v when a = 0 (Where v is the velocity and a is the acceleration.).

Use Rolle's Theorem to show that f(x) = 2x3 + 2x - 6 does not have more than one real root.

Given f(x) = -x5 + 15x4 . Use a graphing utility to estimate the absolute maximum and minimum values of f, if any, on the interval [0, 15].

If f(x) = x4 . Use a graphing utility to estimate the absolute maximum and minimum values of f, if any, on the interval [-1, 2].

Find the relative extrema for f(x) = 8x - sin 2x, 0 < x < π\piπ .

Given f(x) = -2x5 + 20x2 . Use a graphing utility to estimate the absolute maximum and minimum values of f, if any, on the interval [0, 3].

Find the relative extrema for .

Verify that f(x) = x3 - x satisfies the hypothesis of Rolle's Theorem on the interval [-1, 1] and find all values of C in (-1, 1) such that f '(C) = 0

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

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

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

Use Rolle's Theorem to prove that the equation 8x7 - 16x3 + 3 = 0 has at least one solution in the interval (0, 1).

Find the value of c in the interval [0, π\piπ ] that satisfies the Mean Value Theorem. f(x) = sin(8x)

Use a graphing utility to estimate the absolute minimum of f(x) = x4e x on [-1, 1].

Find the dimensions of the rectangle of maximum area which may be embedded in a right triangle with base of 5, height of 12, and hypotenuse of 13 feet as shown in the figure.

The function has

If f(x) = 4x4 - 9x3 , find the intervals where f is concave up and where f is concave down.

If f(x) = 6x4 - 24x3 + 5 , find the intervals where f is increasing and where f is decreasing.

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, 4] that satisfies the Mean Value Theorem. f(x) = 5x² + 20

Given the position function s = 2t³ - 12t² ; find s and v when a = 0 (Where v is the velocity and a is the acceleration.).

Use Rolle's Theorem to show that f(x) = 2x³ + 2x - 6 does not have more than one real root.

Given f(x) = -x⁵ + 15x⁴ . Use a graphing utility to estimate the absolute maximum and minimum values of f, if any, on the interval [0, 15].

If f(x) = x⁴ . Use a graphing utility to estimate the absolute maximum and minimum values of f, if any, on the interval [-1, 2].

Find the relative extrema for f(x) = 8x - sin 2x, 0 < x < $\pi$ .

Given f(x) = -2x⁵ + 20x² . Use a graphing utility to estimate the absolute maximum and minimum values of f, if any, on the interval [0, 3].

Verify that f(x) = x³ - x satisfies the hypothesis of Rolle's Theorem on the interval [-1, 1] and find all values of C in (-1, 1) such that f '(C) = 0

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

Use Rolle's Theorem to prove that the equation 8x⁷ - 16x³ + 3 = 0 has at least one solution in the interval (0, 1).

Find the value of c in the interval [0, $\pi$ ] that satisfies the Mean Value Theorem. f(x) = sin(8x)

Use a graphing utility to estimate the absolute minimum of f(x) = x⁴e ^x on [-1, 1].

If f(x) = 4x⁴ - 9x³ , find the intervals where f is concave up and where f is concave down.

If f(x) = 6x⁴ - 24x³ + 5 , find the intervals where f is increasing and where f is decreasing.