Recall that a function f is even if f(x) = f(x) and oddif f(x) = f(x), for all x in the

Chapter 2, Problem 80

(choose chapter or problem)

Recall that a function \(f\) is even if \(f(-x)=f(x)\) and odd if \(f(-x)=-f(x)\), for all \(x\) in the domain of \(f\). Assuming that \(f\) is differentiable, prove:

(a) \(f^{\prime}\) is odd if \(f\)  is even

(b) \(f^{\prime}\) is even if \(f\) is odd.

Equation Transcription:

Text Transcription:

f

f(-x)=f(x)

f(-x)=-f(x)

x

f

f

f'

f

f'

f