a. Explanation Given information: The given equation is. f ( x ) = x 4 − 2 x 2 o n [ − 2 , 2 ] Calculation: The derivative of given function. f ' ( x ) = 4 x 3 − 4 x f ' ' ( x ) = 12 x 2 − 4 The graph of f ( x ) , f ' ( x ) , f ' ' ( x ) are shown in figure ( a ) b. To determine To find: The graph of f ' ( x ) when f ' ( x ) < 0 . c. To determine To find: The graph of f ' ' ( x ) when f ' ' ( x ) > 0 . d. To determine To find: The graph of f ' ' ( x ) when f ' ' ( x ) < 0 . e. To determine To find: The graph of f ' ( x ) when f ' ( x ) = 0 . f. To determine To find: The graph of f ' ( x ) . g. To determine To find: The graph of f ' ' ( x ) when f ' ' ( x ) = 0 .

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

6th Edition

ISBN: 9781524908102

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Question

Chapter 4, Problem 84SP

To determine

To find: The graph of f'(x) when f'(x)>0 .

To determine

To find: The graph of f'(x) when f'(x)<0 .

To determine

To find: The graph of f''(x) when f''(x)>0 .

To determine

To find: The graph of f''(x) when f''(x)<0 .

To determine

To find: The graph of f'(x) when f'(x)=0 .

To determine

To find: The graph of f'(x) .

To determine

To find: The graph of f''(x) when f''(x)=0 .

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Chapter 4, Problem 83SP

Chapter 4, Problem 85SP

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Find the tangent line approximation 7 to the graph of f at the given point. T(x) = f(x) = csc(x), (8, csc(8)) Complete the table. (Round your answers to four decimal places.) x f(x) T(x) 7.9 7.99 8 8.01 8.1

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Use the information to find and compare Ay and dy. (Round your answers to four decimal places.) Function x-Value Differential of x Ду = dy = y = x² + 2 x = -4 Ax = dx = 0.01

Chapter 4 Solutions

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

Ch. 4.1 - Prob. 1PS Ch. 4.1 - Prob. 2PS Ch. 4.1 - Prob. 3PS Ch. 4.1 - Prob. 4PS Ch. 4.1 - Prob. 5PS Ch. 4.1 - Prob. 6PS Ch. 4.1 - Prob. 7PS Ch. 4.1 - Prob. 8PS Ch. 4.1 - Prob. 9PS Ch. 4.1 - Prob. 10PS

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The graph of f ' ( x ) when f ' ( x ) > 0 .

Solution Summary: The author analyzes the graph of f'(x) when it's 0.

Concept explainers

Videos

To find: The graph of f'(x) when f'(x)>0 .

To find: The graph of f'(x) when f'(x)<0 .

To find: The graph of f''(x) when f''(x)>0 .

To find: The graph of f''(x) when f''(x)<0 .

To find: The graph of f'(x) when f'(x)=0 .

To find: The graph of f'(x) .

To find: The graph of f''(x) when f''(x)=0 .

Want to see the full answer?

Chapter 4 Solutions

The graph of f ' ( x ) when f ' ( x ) &gt; 0 .

Solution Summary: The author analyzes the graph of f'(x) when it's 0.

Concept explainers

Videos

To find: The graph of f'(x) when f'(x)>0 .

To find: The graph of f'(x) when f'(x)<0 .

To find: The graph of f''(x) when f''(x)>0 .

To find: The graph of f''(x) when f''(x)<0 .

To find: The graph of f'(x) when f'(x)=0 .

To find: The graph of f'(x) .

To find: The graph of f''(x) when f''(x)=0 .

Want to see the full answer?

Chapter 4 Solutions

The graph of f ' ( x ) when f ' ( x ) > 0 .