5. (20 points) If f(x) = 2x(x - 1)', with derivatives f'(x) = 2(x - 1) (4x - 1) and "(x) = 12(x - 1)(2x - 1) 4.5 a. (5 points) Find lim f(x) and lim f(x) x-+0 X4-00 b. (5 points) On what intervals is f (x) increasing? On what intervals is f(x) decreasing?c. (5 points) On what intervals is f (x) concave up? On what intervals is f (x) 4 concave down? d. (5 points) Graph the function below. Show asymptote(s), intercepts, and the exact points (x and y coordinates) where the function has any local maximum, local minimum values, or points of inflection