Suppose that I = (−a, a) for some a > 0. A function f : I → R is said to be even if and only if f (−x) = f (x) for all x ∈ I, and said to be odd if and only if f (−x) = −f (x) for all x ∈ I .
a) Prove that if f is odd and differentiable on I, then f′ is even on I .
b) Prove that if f is even and differentiable on I, then f′ is odd on I .
We need at least 10 more requests to produce the solution.
0 / 10 have requested this problem solution
The more requests, the faster the answer.