1. (15 points) Let f(x) = 23 +3x2 -24x. Find the intervals of increase/ decrease, any local extrema, the intervals of concavity, and any points of inflection. 2. (10 points) Find and classify all local extrema (as either local maxima or minima) f (x) = 72+9 3. (10 points) Find f(x) if f"(x) = 24x + sin x, f(0) = 0, f'(0) = -4, and f"(0) = 4. 4. (15 points) A farmer with 800 feet of fencing wants to enclose a rectangular area, and then divide that area into 3 pens using fencing parallel to one of the sides of the rectangle. How much area can he enclose? 5. (15 points) A stone was dropped from the top of a 512-foot-high cliff. With what velocity will it strike the ground below? (Assume g = =32 feet per second squared.) 6. (15 points) Evaluate the integral / (1 + x - x2) dx using the limit definition (i.e., Riemann sums). Also: CHECK YOUR ANSWER using the fundamental theorem of calculus. [Note that 1 = n; Finn+1) Fin(n + 1)(2n + 1) i= 1 6 i=1 7. (20 points) Evaluate the following: sin z (a) do cos ( 1 2 ) at ( b ) (2 + 5 )(x -3) dx. ( c ) 3 + 1 -dx. (d ) x2 Vx - Idx. (u = Vx- 1)