37. If f(a) = 2 and g(x) = 1 + ax, a ER, what value of a makes the derivative of f(g(ac)) at * = 0 equal to 2? (A) (B) In(2) (C) 3 (D) 3 (E) In(2) ca.38. A production facility is capable of producing 500 computer components in a clay, and the total daily cost of producing :13 components is given by, 00,000 :13 C(33) = 3009 + 6:13 + How many computer components should they produce per day in order for the marginal cost to be zero? (A)222 Pi (B) 100 : (D) 150 \":2\"; ::::=: (E)175 \"2%; Lafg 39. Consider a function y : f(:r:) such that d zwzmH. d2: Application of the First Derivative Test yields that we have ? (A no critical points (B a local minimum at as = 4 ) ) (C) a local maximum at a: = 4 (D) neither a local maximum nor a local minimum at an = 4 ) (E a point of inflection at a: = 4 40. Consider the function f(:13) = 2m3 9:122 243: + 1 Application of the Second Derivative Test yields ? (A) f(4) is a point of inflection (B) f(3/2) is a local maximum (C) the test is inconclusive at a: = 3/2 (D) f(1) is an absolute minimum (E) f(l) is a local minimum