Question: Suppose that I = (-a, a) for some a > 0. A function f : I R is said to be even if and

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 f, then f' is even on I.
b) Prove that if f is even and differentiable on f, then f' is odd on f.

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