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 17RE
To determine

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

Expert Solution

Answer to Problem 17RE

The answer is shown below.

Explanation of Solution

Given information:

The function is f(x)=3x65x5+x45x32x2+2 .

Calculation:

Consider the equation.

  f(x)=f(x)=3x65x5+x45x32x2+2

Differentiate above equation.

  f(x)=18x525x4+4x315x24x

And,

  f(x)=90x4100x3+12x230x4

The graph f(x) is shown figure-1

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 4, Problem 17RE , 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 17RE , additional homework tip  2

Figure-2

The extreme value for f(0.23)=1.96,f(0)=0 and f(1.62)=19.2

The graph f(x) is shown figure-3

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 4, Problem 17RE , additional homework tip  3

Figure-3

Therefore the inflection points for f(x) are (0.12,1.98),(1.24,12.1)

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