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 19RE
To determine

To find: The inflection point for the given function.

Expert Solution

Answer to Problem 19RE

The inflection point for the given function is (±23,e32) .

Explanation of Solution

Given information:

The function is f(x)=e1x2 .

Calculation:

Consider the equation.

  f(x)=e1x2

The graph f(x) is shown figure-1

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 4, Problem 19RE

Figure-1

Differentiate above equation.

  f(x)=(2)x3e1x2=2x3e1x2

And,

  f(x)=2[x3(2x3)e1x2+e1x2(3x4)]=2x6e1x2(23x2)

Substitute f(x)=0 in above equation.

  2x6e1x2(23x2)=023x2=0x=±23

Substitute x=±23 in above equation.

  y=e32

Thus, the point of inflection is (±23,e32)

Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!