EVT Practice (4 questions/Please show work)

4. [2009 BCZ, part b only] The rate at which people enter an auditorium for a rock concert is modeled by the function R given by R(t) = 1380:2 675:3 for 0 g t 5 2 hours. R(t) is measured in people per hour. No one is in the auditorium at time t = 0, when the doors open. The doors close and the concert begins at time t = 2. b. Find the time when the rate at which people enter the auditorium is a maximum. Justify your answer. 1. Let g be a continuous function on the closed interval [0, 1]. Let g(0) = 1 and g(1) = 0. Which of the following is not necessarily true? (A) There exists a number h in [0, 1] such that g(h) 2 g(x) for all x in [0, 1]. (B) For all a and b in [0, 1], if a = b, then g(a) = g(b) (C) There exists a number h in [0, 1] such that g(h) = (D) There exists a number h in [0, 1] such that g(h) = N/W NI - (E) For all h in the open interval (0, 1), lim g(x) = g(h) x-th [BC73 #18] 2. The absolute maximum value of f(x) =x -3x2 +12 on the closed interval [-2, 4] occurs at x = (A) 4 (B) 2 (C) 1 (D) O (E) -2 [AB88 #33] 3. The function f is continuous for -2