# The inflection point for the given function.

### Single Variable Calculus: Concepts...

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

### 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

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

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)

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