Analytically determine the extrema of f(x) = -(x-2)³ on [-1,4] Analytically determine: a) the extrema of f(x) = x(x - 2)² b) the intervals on which the function is increasing or decreasing. Give an example function (and sketch of the function you choose) that has a critical point that is NOT an extreme value. 4. Find the values of 'c' that satisfy the Mean Value Theorem for Derivatives for f(x) = 2x³ - 2x the interval [1, 3].