Question

Let f: R-->R. Prove,
If f is diffenrentiable at c such that f(c) = 0, then g(x) = |f(x)| is differentiable at c if and only if
f′(c) = 0.

Answer 1

Do i prove this in cases?
1st: f is diff at c such that f(c) = 0 and f′(c) = 0 ==> g(x) is diff at c.
2nd: f is diff at c sucht that f(c) = 0 and g(x) = |f(x)| diff at c ==> f′(c) = 0.