periodic Function

[ffuh205]

If a function is periodic with a period of K, then its derivative is periodic with the same period K.

A. Mostly false, but is true once in awhile

B. Mostly true, there are a few exceptions

C. Always false, 100% of the time.

D. Always True, 100% of the time

I know that b is false.

 

[Deleted member 4993]

If a function is periodic with a period of K, then its derivative is periodic with the same period K.

A. Mostly false, but is true once in awhile

B. Mostly true, there are a few exceptions

C. Always false, 100% of the time.

D. Always True, 100% of the time

I know that b is false.

In general, a periodic function is a function that satisfies:

f(x) = f(x + b)

 

[daon]

Let f be a periodic function of period p. This means f(x)=f(x+kp) for all x, and for all integers k. Take the derivative of each side.

I'd be cautious though. Periodic functions need not be continuous, and hence may not be differentiable.