Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = e−5x, [0, 3] Yes, f is continuous and differentiable on double-struck R, so it is continuous on [0, 3] and differentiable on (0, 3) . No, f is continuous on [0, 3] but not differentiable on (0, 3). There is not enough information to verify if this function satisfies the Mean Value Theorem. No, f is not continuous on [0, 3]. Yes, it does not matter if f is continuous or differentiable; every function satisfies the Mean Value Theorem.