Question: Suppose that f : R R is differentiable at c and that f(c) = 0. Show that g(x) := |f(x)| is differentiable at c

Suppose that f : R → R is differentiable at c and that f(c) = 0. Show that g(x) := |f(x)| is differentiable at c if and only if fʹ(c) = 0.

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