BuyFind

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 4, Problem 16RE
To determine

To graph and to estimate the intervals of increase, decrease and inflexion points.

Expert Solution

Explanation of Solution

Given:

The given function is f(x)=x3xx2+x+3

Calculation:

  f(x)=x3xx2+x+3

  f'(x)=x4+2x3+10x23(x2+x+3)2f''(x)=6(x33x212x1)(x2+x+3)3

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 4, Problem 16RE , additional homework tip  1

From the above graph it can be estimated that f is increasing on (,0.57) and (0.52,)

Decreasing on (0.57,0.52)

There is a local maximum at f(0.57)=0.17

And a local minimum at f(0.52)=0.1

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 4, Problem 16RE , additional homework tip  2

The inflexion points are and (2.21,2.09) and (0.09,0.03)

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