1. Determine if Rolle's Theorem applies to the function on the given interval. If it does, find the point ( c ) guaranteed to exist by Rolle's Theorem. a. f(x) = sin2x on the interval [0, pi /2] Does Rolle's apply? If so, what is c? b. f(x) = x^3 - x^2 - 5x - 3 on the interval [-1,3] Does Rolle's apply?. If so, what is c? 2. F(x) = x^3 - 2x^2 is differentiable and continuous on the interval [0, 1]. Find the point c on the interval [0 , 1] such that c satisfies the Mean Value Theorem. 3. Using the First Derivative Test state the intervals in which f(x) = x^4- 4x^3 + 4x^2 is increasing and decreasing. Interval(s) increasing _________ Interval(s) decreasing _________ 4. Using the Second Derivative Test state the interval(s) f(x) = x^4 - 2x^3 + 1 is concave up and concave down and identify any inflections points. Interval(s) concave up ________ Interval(s) concave down _________