How to tell if a function is differentiable on an interval?

To see this, consider the everywhere differentiableand everywhere continuous function g (x) = (x-3) * (x+2) * (x^2+4). To prove that g' has at least one zero for x in (-∞, ∞), notice that g (3) = g (-2) = 0. By Rolle's Theorem, there must be at least one c in (-2, 3) such that g' (c) = 0. as example