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.