Rolle's Theorem Determine whether Rolle's Theorem applies to the following fimctions on the given interval. If so, find the point(s) guaranteed to exist by Rolle's Theorem. h(x) =e;[-a, a], where a > 0 Mean Value Theorem Consider the following functions on the given interval [a, b]. Determine whether the Mean Value Theorem applies to the following functions on the given interval [a, b]. If so, find the point(s) that are guaranteed to exist by the Mean Value Theorem. f(x)=x -2x; 10, 1] Without evaluating derivatives, determine which of the functions f(x) = Inx, g(x) = in 2 x, h(x) = In x3, and p(x) =In 10 x2 have the same derivative. Mean Value Theorem and graphs Find all ports on the mierval (1, 3) at which the slope of the tangent ime equals the average rate of change off on [1, 31. Reconcile your results with the Mean Value Theorem