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
