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 17RQ
To determine

 whether the statement, if f is periodic, then f’ is periodic is true or false.

Expert Solution

Answer to Problem 17RQ

The given statement is true.

Explanation of Solution

Given that f(x) is periodic.

If f(x) is periodic for a number p, then f(x+p)=f(p) . (1)

Differentiate the equation (1),

f(x)=f(x+p)f'(x)=f'(x+p)(1)f'(x)=f'(x+p)

Thus, f'(x) is periodic.

Therefore, the given statement is true.

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