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 18RE
To determine

To find: The intervals where the extreme value is increasing and decreasing.

Expert Solution

Answer to Problem 18RE

The answer is shown below.

Explanation of Solution

Given information:

The function is f(x)=x2+6.5sinx .

Calculation:

Consider the equation.

  f(x)=x2+6.5sinx

Differentiate above equation.

  f(x)=2x+6.5cosx

And,

  f(x)=26.5sinx

The graph f(x) is shown figure-1

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 4, Problem 18RE , additional homework tip  1

Figure-1

The absolute maximum value is f(1)=10

The absolute minimum value is f(1.8)=18

The graph f(x) is shown figure-2

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 4, Problem 18RE , additional homework tip  2

Figure-2

The graph f(x) is shown figure-3

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 4, Problem 18RE , additional homework tip  3

Figure-3

The function is decreasing for 5<x<1.25,2.5<x<3.25 and increasing on 1.25<x<2.5,3.25<x<5 and the inflection points for f(x) are (3.5,15),(0.3,2),(2.7,10)

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