1. does the function satisfy the hypotheses of the mean value theorem on the given interval? f(x) = e−2x, [0, 1]yes, f is continuous and differentiable on double-struck r, so it is continuous on [0, 1] and differentiable on (0, 1) .there is not enough information to verify if this function satisfies the mean value theorem. no, f is not continuous on [0, 1].yes, it does not matter if f is continuous or differentiable; every function satisfies the mean value theorem. no, f is continuous on [0, 1] but not differentiable on (0, 1).if it satisfies the hypotheses, find all numbers c that satisfy the conclusion of the mean value theorem. (enter your answers as a comma-separated list. if it does not satisfy the hypotheses, enter dne).c = ? 2. verify that the function satisfies the three hypotheses of rolle's theorem on the given interval. then find all numbers c that satisfy the conclusion of rolle's theorem. (enter your answers as a comma-separated list.)f(x) = x3 − x2 − 6x + 9, [0, 3]c =