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Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 2, Problem 44RE

(a)

To determine

To graph: For the function f'' .

Expert Solution

Explanation of Solution

Given information:

The given graph of the derivative f' of f is shown in figure (1).

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 2, Problem 44RE , additional homework tip  1

Figure (1)

Graph:

The graph of f'' is positive when f' is increasing and negative when f' is negative.

All the local extremes, f''(x)=0 .

The plot for local extremes is shown in figure (2).

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 2, Problem 44RE , additional homework tip  2

Figure (2)

The plot for f'' is shown in figure (3).

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 2, Problem 44RE , additional homework tip  3

Figure (3)

Interpretation: Graph for the function f'' is shown in figure (3).

(b)

To determine

To graph: For the function f .

Expert Solution

Explanation of Solution

Given information:

The given graph of the derivative f' of f is shown in figure (1).

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 2, Problem 44RE , additional homework tip  4

Figure (1)

Graph:

The function f is snit-derivative of f' . It has local extremes when f'(x)=0 .

While it is increases when f'(x)>0 and decreases when f'(x)<0 . Start fromleft and the graph of f is shown in figure (4).

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 2, Problem 44RE , additional homework tip  5

Figure (4)

Interpretation: Graph for the function f'' is shown in figure (4).

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