You may use a calculator, but no books or notes. The point value of each problem is given in the left-hand margin. (10 pts. ) Let y = f (x) = x4 8x3 + 18x2. (a) find all critical numbers. (b) explain what the second derivative test says about each critical number. (8 pts. ) Find the x and y coordinates of the absolute maximum of the function y = x3 3x on the closed interval 0 x 2. The position of a moving particle is given by x = 4 t+1 . Find the instant of time in the interval 0 t 3 when the instantaneous velocity is equal to the average velocity over this interval. (7 pts. ) Z x8 x2 + 4 x3 dx. 2x 1dx using four rectangles and left (8 pts. ) Find the x coordinate of the in ection point of the function y = f (x) = x5 + 5x4.
