Suppose we have a continuous, differentiable function with the following properties: lim f(x) = -2 lim f(x) = -2 1'(3) = 0 f(x) < 0 on the interval (1,5). 1(x) > 0 on the intervals ( -1) and (5,6). (a) (4 points) Sketch a possible graph of f. (b) (2 points) From our given information, does f definitely have an absolute maximum? If so, where does it occur? 3. At t=0 seconds, a bowling ball is dropped from a plane. Exactly 12 seconds after it was dropped (at t = 12), the ball has a downward velocity of 384 feet per second, and is 2000 feet above the ground. (a) (2 points) Use the above information to find the linearization of the ball's position at t = 12. (b) (2 points) Use this linearization to find the height of the ball at t = 11.5 seconds,