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 5.4, Problem 27E

a.

To determine

To find: The values of x.

Expert Solution

Answer to Problem 27E

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

Answer to Problem 27E

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

Answer to Problem 27E

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

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