4.1 Optimization on an Interval Find the derivative, and use this to find the critical points. Then find the maximum and minimum of the given function on the given interval. A. f(x) = x3 12 x on the interval [-1,4] B. ['00 = x3 6 Jr2 + 6 x 4 on the interval [-1,4] x x2+1 C. 900 = on the interval [1, 5] What happens if we adjust to the interval [1, 0 )? 4.2 Rolle's Theorem and Mean Value Theorem Can you state Rolle's Theorem? the Mean Value Theorem? Do you know what these are used for? Why do Rolle's Theorem (and the Mean Value theorem) apply to any polynomial on any interval (a,b)? [Do you recall using Rolle's theorem from Precalculus?] A. Apply Rolle's Theorem to the function f(x) = 4x Jr2 on the interval [0,4]. State the conclusions. Then find all the values of c that satisfy f'lc) = O