BE SURE YOU ARE USING PAGE 3 OF THE ANSWER SHEET TO RECORD YOUR ANSWERS TO QUESTIONS NUMBERED 76-92 . . YOU MAY NOT RETURN TO PAGE 2 OF THE ANSWER SHEET. In this exam: (I) The exact numerical value of the correct answer does not always appear among the choices given. When this happens, select from among the choices the number that best approximates the exact numerical value. (2) Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers x for which f(x) is a real number. (3) The inverse of a trigonometric function f may be indicated using the inverse function notation f -1 or with the · prefix "arc" (e.g., sin - I x = arcsin x ). Unauthorized copying or reuse of any part of this page is illegal. -24-GO ON TO THE NEXT PAGE.

B B B B B B B B B y ------+-----1----+-x 0 Graph off 76. The function f, whose graph is shown above, is defined on the interval - 2 ~ x ~ 2. Which of the following statements about f is false? (A) f is continuous at x = 0. ® is differentiable at x = 0. (C) f has a critical point at x = 0. (D) f has an absolute minimum at x = 0. (E) The concavity of the graph of f changes at x = 0. 77. Let f and g be. the functions given by f(x) = ex and g(x) = x4. On what intervals is the rate of change of f(x) greater than the rate of change of g(x)? (A) (0.831, 7.384) only @(-oo, 0.831) and_ (7.384, oo) (C) (-oo, -0.816) and (1.430
, 8.613)
Unauthorized copying or reuse of any part of this page is illegal. Lt I. CA .• ,t:-. UJt -25-o -4x 3 i ~ , f ,,J'j j,j !, , iD GO ON TO THE NEXT PAGE.

B B B B B B B B B y -- 3 --2 -- 1 / ....................-I 0 1 V 3 4 5 6 7 8 9 X - I -- 2 Graph off 78. The graph of the piecewise linear function f is shown above. What is the value of f9 (3f(x) + 2) dx? - I C (A) 7.5 .,... (B) 9.5 J:§.)1.s (D) 47 (E) 48.5 , 3J f(x)oi, 4 f ;2, c, :: 5 (-J h r i < h>u~ 2 )I: f; ') , 1 I\ ( 1 9. ~ 27 --' -I") , "' 2 ?, r_· -f ... -"> (-2---l:} -t~· L t J _. j · ~;; -r vO :,; ~ ,, -
79. Let f be a function having derivatives of all orders for x > 0 such that /(3) = 2, f'(3) = -1, / "(3) = 6, and /"'(3) = 12. Which of the following is the third-degree Taylor polynomial for f about x = 3.? ., ' ... . .,
(C) 2 - (x - 3)+6(x - 3)2+ 12(x - 3)3 ~ 3 ---2 3 ®,,.,-'2 -(x -3) + 3(x -3) + 2(x -3) Unauthorized copying or reuse of any part of this page is illegal. 2 ~ , :, GO ON TO THE NEXT PAGE. -26-

B B B B B B B B B y Graph of .f' 80. The graph of f', the derivative of the function f, is shown above. Which of the following statements must be true? I. f has a relative minimum at x = - 3. -r r-_...:-II. The graph off has a point of inflection at x = -2. I III. The graph off is concave down for O < x < 4. I (A) I only (B) II only Unauthorized copying or reuse of any part of this page is illegal. (C) III only (D) I and II only -27-§) and III only GO ON TO THE NEXT PAGE.

B B · B B B B. B B B 0<x<l l<x<2 J(x) Positive Negative f'(x) Negative Negative f"(x) Negative Positive 8 1. Let f be a function that is twice differentiable on -2 < x < 2 and satisfies the conditions in the table above. If J(x) = f(- x ), what are the x-coordinates of the points of inflection of the graph off on - 2 < x < 2?