# The values of x. ### 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 5.4, Problem 27E

a.

To determine

## To find: The values of x.

Expert Solution

The value of x for which the function have a local maxima value is ±1 .

### Explanation of Solution

Given information: 0xsin(πt22)dt

Calculation:

f(s)=sin(πt22)f'(s)=(π2)(2)cos(πt22)f'(s)=πcos(πt22)

For finding local maxima,

πcos(πt22)=0πcos(πt22)=cos(π2)

Comparing both side,

πt22=π2t2=1t=±1

Hence, The value of x for which the function have a local maxima value is ±1

b.

To determine

### To find: The interval where the function concave upword.

Expert Solution

The interval is 1t2 .

### Explanation of Solution

Given information: 0xsin(πt22)dt

Calculation: 0xsin(πt22)dt

The function concave upward when,

π2πt22π

Therefore,

1t22=1t2

Hence, The interval is 1t2 .

c.

To determine

### To solve: The equation.

Expert Solution

The solution of the equation is x=1.4

### Explanation of Solution

Given information: 0xsin(πt22)dt

Calculation: 0xsin(πt22)dt

S(x)0xsin(πt22)dt=0.2      S(x)S(0)=0.2      x=1.4

Hence, The solution of the equation is x=1.4

### 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!