Consider the function g(x)=∣x∣ on the closed interval [−1,1]. Which statement identifies the hypothesis that prevents the Mean Value Theorem from guaranteeing a number c in (−1,1) with g′(c)=0?
a) g is not continuous on [−1,1].
b) Since g(−1)=g(1), Rolle's Theorem applies instead, so the Mean Value Theorem does not.
c) g is not differentiable on (−1,1).
d) The average rate of change of g on [−1,1] is not zero.