1. (5 points) For the following functions defined on the given intervals, check if the Rolle's theorem can be applied to f on [a, b]. If so, then find c in (a, b) such that f' (c) = 0. (a) (2 points) f(x) = x2 on [2, 3]. (b) (3 points) f(x) = sin(x) on [4 3x ]2. (5 points) Define the function f (x) = x3 2x. (a) (2 points) Find the average slope of this function on the interval [2,4]. (b) (3 points) Find all value(s) of c in [2,4] such that f'(c) is equal to the average slope you find in Part (a). 3. (5 points) Let f (x) = x3 + 2x 7. Find out where f is increasing and where f is decreasing. 4. (5 points) Let f(x) = x2 - 2x4. Find out all relative maxima and relative minima of f