4 at 1 1:00am. Name: For each question below, please show all of your work. Good luck! (0) (3 Points) Correct notation used through the exam. (1) (20 Points) Compute the following integrals (a ) 23 + 4 + 3 ) dx (b ) J ( 2 2 + 20 + 1 ) do (2) (20 Points) Suppose a continuous function f(r) has first and second deriva- tives given by f'(x) = 2(x + 5)(x - 3) and f"(x) = 4x + 4 (a) Find the intervals on which f(r) is increasing. (b) Find the intervals on which f(x) is decreasing. (c) Find the x-values of the local maxima of f(x). (d) Find the r-values of the local minima of f(x). e) Find the intervals on which f (x) is concave up. f) Find the intervals on which f(x) is concave down. g) Find the r-values of the inflection points of f(r). (3) (20 Points) Compute the following limits sin(x) - 322 -x -5x - 9 (a) lim -2 cos(I) + 2 (b) lim x-+0 2 In(x) - 4 (4) (15 Points) Suppose an object has velocity function given by v ( t ) = 14 - 3t + 9 -7 cos (t) and has initial position s(0) = -6. Find the position function, s(t). (5) (10 Points) Use the graph of y = f(r) below to compute the following integral ( a ) [ f ( x )do (6) (15 Points) We are constructing an open-top box with a square base. If we have 45 square meters of material, what is the maximum volume of such a box