Question 1

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 2

The equation, x3 - x2 - 4x - 4 = 0 has one real solution for 1 < x < 4. Approximate it by Newton's Method. Use 3 for your initial value and calculate eight iterations.

Accepted Answer

f(x) = x³-x

Question 3

An isosceles triangle is drawn with its vertex at the origin and its base parallel to the x axis. The vertices of the base are on the curve 6y = 30 - x2. Find the area of the largest such triangle.

Accepted Answer

The answer of An isosceles triangle is drawn with its...

Question 4

Verify that f(x) = x3 -5x + 4 satisfies the hypothesis of the Mean-Value Theorem over the interval [-2, 3] and find all values of C that satisfy the conclusion of the theorem.

Accepted Answer

f(-2) = 6
f(3) = 8
f

Question 5

Given f(x) = 20x3 -12x2 - 3x + 9, find the intervals where f is concave up and where f is concave down.

Accepted Answer

The answer of Given f(x) = 20x3 -12x2 - 3x...

Question 6

If f(x) = x(x - 7)5 , find the intervals where f is concave up and where f is concave down.

Accepted Answer

Concave up

Question 7

Sketch the graph of y = 4 - 2x- x2. Find any stationary points and any points of inflection.

Accepted Answer

y' = -2 -2

Question 8

If f(x) = x4 - 19x3 + 39 , find the location of any inflection points.

Accepted Answer

The answer of If f(x) = x4 - 19x3 +...

Question 9

Answer true or false. If a particle is dropped a distance of 619 m. It has a speed of 110.16 m/s (rounded to the nearest hundredth of a m/s) when it hits the ground.

Accepted Answer

A) True 
 B)False

Question 10

Does   satisfy the hypothesis of the Mean-Value Theorem over the interval [0, 6]? If so, find all values of C that satisfy the conclusion of the theorem.

Accepted Answer

No, f is not continu

Question 11

Find the value of c in the interval [0, 2 $\pi$] that satisfies the Mean Value Theorem. f(x) = 6 cos x

Accepted Answer

@#IMG-DLM& = 0
f '(x

Question 12

Given   . Find any stationary points and points of inflection.

Accepted Answer

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

Question 13

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 at @#IMG-DLM& Inflect

Question 14

Does   satisfy the hypothesis of the Mean-Value Theorem over the interval [0, 1]? If so, find all values of C that satisfy the conclusion.

Accepted Answer

Yes, since f is continuous ove

Question 15

Given the position function s = 2t3 -6t2 + 5t + 4; find s and v when a = 0 (Where v is the velocity and a is the acceleration.).

Accepted Answer

v = 6t² - 12t + 5 a

Question 16

Use Newton's Method to find the largest positive solution of x5 + 6x3-3x2 - 9 = 0. Use 3 for your initial value and calculate three iterations.

Accepted Answer

A)  2.3278689 
B)  1.8122908 
C)  1.4559632 
D)  1.4558412 
E)  1.4559512 
A)  2.3278689 
B)  1.8122908 
C)  1.4559632 
D)  1.4558412 
E)  1.4559512

Question 17

Answer true or false.   on [-2, 2] satisfies the hypotheses of Rolle's Theorem.

Accepted Answer

A) True 
 B)False

Question 18

Use Newton's Method to find the largest solution of x5 - 2x4 + 5x3 -x2 + 7x + 12 = 0. Use 2 for your initial value and calculate six iterations.

Accepted Answer

A)  1.2151899 
B)  0.0852538 
C)  -1.7308568 
D)  -1.0071278 
E)  -1.2897963 
A)  1.2151899 
B)  0.0852538 
C)  -1.7308568 
D)  -1.0071278 
E)  -1.2897963

Question 19

The derivative of a continuous function is f '(x) = 4(x -7)2(4x + 4). Find all critical points and determine whether a relative maximum, relative minimum or neither occurs there.

Accepted Answer

Critical points are x = 7 and

Question 20

A divided field is to be constructed with 7640 feet of fence as shown.
For what value of x will the area be a maximum?

Accepted Answer

x = 1910 f

The function has

The equation, x³ - x²- 4x - 4 = 0 has one real solution for 1 < x < 4. Approximate it by Newton's Method. Use 3 for your initial value and calculate eight iterations.

An isosceles triangle is drawn with its vertex at the origin and its base parallel to the x axis. The vertices of the base are on the curve 6y = 30 - x². Find the area of the largest such triangle.

Verify that f(x) = x³ -5x + 4 satisfies the hypothesis of the Mean-Value Theorem over the interval [-2, 3] and find all values of C that satisfy the conclusion of the theorem.

Given f(x) = 20x³ -12x² - 3x + 9, find the intervals where f is concave up and where f is concave down.

If f(x) = x(x - 7)⁵ , find the intervals where f is concave up and where f is concave down.

Sketch the graph of y = 4 - 2x- x². Find any stationary points and any points of inflection.

If f(x) = x⁴ - 19x³ + 39 , find the location of any inflection points.

Answer true or false. If a particle is dropped a distance of 619 m. It has a speed of 110.16 m/s (rounded to the nearest hundredth of a m/s) when it hits the ground.

Does satisfy the hypothesis of the Mean-Value Theorem over the interval [0, 6]? If so, find all values of C that satisfy the conclusion of the theorem.

Find the value of c in the interval [0, 2 $\pi$ ] that satisfies the Mean Value Theorem. f(x) = 6 cos x

Given . Find any stationary points and points of inflection.

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

Does satisfy the hypothesis of the Mean-Value Theorem over the interval [0, 1]? If so, find all values of C that satisfy the conclusion.

Given the position function s = 2t³ -6t² + 5t + 4; find s and v when a = 0 (Where v is the velocity and a is the acceleration.).

Use Newton's Method to find the largest positive solution of x⁵ + 6x³-3x² - 9 = 0. Use 3 for your initial value and calculate three iterations.

Answer true or false. on [-2, 2] satisfies the hypotheses of Rolle's Theorem.

Use Newton's Method to find the largest solution of x⁵ - 2x⁴ + 5x³ -x² + 7x + 12 = 0. Use 2 for your initial value and calculate six iterations.

The derivative of a continuous function is f '(x) = 4(x -7)²(4x + 4). Find all critical points and determine whether a relative maximum, relative minimum or neither occurs there.

A divided field is to be constructed with 7640 feet of fence as shown. For what value of x will the area be a maximum?

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 function has

The equation, x3 - x2 - 4x - 4 = 0 has one real solution for 1 < x < 4. Approximate it by Newton's Method. Use 3 for your initial value and calculate eight iterations.

An isosceles triangle is drawn with its vertex at the origin and its base parallel to the x axis. The vertices of the base are on the curve 6y = 30 - x2. Find the area of the largest such triangle.

Verify that f(x) = x3 -5x + 4 satisfies the hypothesis of the Mean-Value Theorem over the interval [-2, 3] and find all values of C that satisfy the conclusion of the theorem.

Given f(x) = 20x3 -12x2 - 3x + 9, find the intervals where f is concave up and where f is concave down.

If f(x) = x(x - 7)5 , find the intervals where f is concave up and where f is concave down.

Sketch the graph of y = 4 - 2x- x2. Find any stationary points and any points of inflection.

If f(x) = x4 - 19x3 + 39 , find the location of any inflection points.

Answer true or false. If a particle is dropped a distance of 619 m. It has a speed of 110.16 m/s (rounded to the nearest hundredth of a m/s) when it hits the ground.

Does satisfy the hypothesis of the Mean-Value Theorem over the interval [0, 6]? If so, find all values of C that satisfy the conclusion of the theorem.

Find the value of c in the interval [0, 2 π\piπ ] that satisfies the Mean Value Theorem. f(x) = 6 cos x

Given . Find any stationary points and points of inflection.

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

Does satisfy the hypothesis of the Mean-Value Theorem over the interval [0, 1]? If so, find all values of C that satisfy the conclusion.

Given the position function s = 2t3 -6t2 + 5t + 4; find s and v when a = 0 (Where v is the velocity and a is the acceleration.).

Use Newton's Method to find the largest positive solution of x5 + 6x3-3x2 - 9 = 0. Use 3 for your initial value and calculate three iterations.

Answer true or false. on [-2, 2] satisfies the hypotheses of Rolle's Theorem.

Use Newton's Method to find the largest solution of x5 - 2x4 + 5x3 -x2 + 7x + 12 = 0. Use 2 for your initial value and calculate six iterations.

The derivative of a continuous function is f '(x) = 4(x -7)2(4x + 4). Find all critical points and determine whether a relative maximum, relative minimum or neither occurs there.

A divided field is to be constructed with 7640 feet of fence as shown. For what value of x will the area be a maximum?

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

The equation, x³ - x²- 4x - 4 = 0 has one real solution for 1 < x < 4. Approximate it by Newton's Method. Use 3 for your initial value and calculate eight iterations.

An isosceles triangle is drawn with its vertex at the origin and its base parallel to the x axis. The vertices of the base are on the curve 6y = 30 - x². Find the area of the largest such triangle.

Verify that f(x) = x³ -5x + 4 satisfies the hypothesis of the Mean-Value Theorem over the interval [-2, 3] and find all values of C that satisfy the conclusion of the theorem.

Given f(x) = 20x³ -12x² - 3x + 9, find the intervals where f is concave up and where f is concave down.

If f(x) = x(x - 7)⁵ , find the intervals where f is concave up and where f is concave down.

Sketch the graph of y = 4 - 2x- x². Find any stationary points and any points of inflection.

If f(x) = x⁴ - 19x³ + 39 , find the location of any inflection points.

Find the value of c in the interval [0, 2 $\pi$ ] that satisfies the Mean Value Theorem. f(x) = 6 cos x

Given the position function s = 2t³ -6t² + 5t + 4; find s and v when a = 0 (Where v is the velocity and a is the acceleration.).

Use Newton's Method to find the largest positive solution of x⁵ + 6x³-3x² - 9 = 0. Use 3 for your initial value and calculate three iterations.

Use Newton's Method to find the largest solution of x⁵ - 2x⁴ + 5x³ -x² + 7x + 12 = 0. Use 2 for your initial value and calculate six iterations.

The derivative of a continuous function is f '(x) = 4(x -7)²(4x + 4). Find all critical points and determine whether a relative maximum, relative minimum or neither occurs there.