Given that f {I} and its inverse, 34"] {I} are differentiable functions with f (I) and 3\" [3) values at x = 2 x = 3 and x = 4 as indicated in the table, find the derivative of 3"] {I} at x = 2. egg \fWhat of the following best represents the left-end behavior model of the function VO A. g(x) = x2 - 2x XO B. g(x) = a2 -. XO C. g(x) =x2 XO D. g(x) =2 + XO E. g(x) = x2 +2x{22+z2] Sink1} 1342142: have a removable For which of the following intervals does the function f {I} = discontinuity? x A. [25,1.5] x e. [15, 41.5] x (3. [415,115] v o. [05,15] x E. [15,-2.5] This question has two parts. First, answer PartA. Then, answer Part B. Part A You are given a continuous polvnomial function f (I) with select values shown in the table. What is the minimum number of values ofx where f (s) = D? X HE X El X {3.1 V [13 Part B For the same continuous polynomial function f (I) with select derivative values shown in the table. what is the minimum number of values ofx vvhere the slope of f {I} is zero? X AD X B1 X {3.2 V' I13 \fThis question has two parts. First, answer Part A. Then, answer Part B. Part A What is f' (x) given that f (x) = x2 Inx - x? XO A f' (x) = 2xInc XO B. f' (x) = alnx+x-1 xo c. f' (x) = 2xInx-x-1 VO D. f'(x) = 2xInx+x-1 XO E. f' (x) = 2xInx + 2x -1 Part B What is f" (a)? XO A f" (x) = 2Inx+1 XO B. f" (x) = 2Inx+2 VO C. f" (x) = 2lnx + 3 XO D. f" (x) = 2Inx + 2x+1 XO E. f" (x) = 2Inx + 2x +3This question has two parts. First, answer Part A. Then, answer Part B. Part A A polynomial function p () has degree 3. What shape will p' (a) have? X O A. a straight line with a nonzero slope X O B. a horizontal line VO C. a parabola X O D. a vertical line X O E. cannot be determined Part B A polynomial function p () has degree 3. What shape will p" (x) have? X O A. a straight line with a nonzero slope V O B. a horizontal line X O C. a parabola X O D. a vertical line X O E. cannot be determinedThis question has two parts. First, answer Part A. Then, answer Part B. Part A Where does f (x) = + 3x2 - 5x - 2 have a local maximum? XO A 1 = 1+ 2V/6 3 XO B. .=-1- V6 3 xO C. .=-1+ V6 3 VO D. . = -1 - 26 3 XOE. . r =-1 + 2v6 3 Part B What is the x-value of the inflection point of f (a)? VO Ac=-1 XO B. * = - XO C. X= 0 XO D. .= XO E. X= 1This question has two parts. First, answer Part A. Then, answer Part B. Part A Suppose you are given the function f (x) = sin x + bcosx. Which of the following relationships will ensure that a local extremum occurs at x = k in the interval (0, ?)? XO A. b= -2 cot k XO B. b = - cot k XO C. b= - tank VO D. b = cot k XO E. b = tank Part B Which of the following relationships will ensure that an inflection point occurs at x = k in the interval (0, 7)? XO A. b = -2 cot k XO B. b= - cot k VO C. b= - tank XO D. b = cot k XO E. b = tankThis question has two parts. First. answer PartA. Then, answer Pait B. Part A Suppose you are given the function f (1:) = 33 24:32: + 1. Which of the following best represents the location of the global minimum of the function? X A. :I: : U.48 X El. I = U.12 X C. X = [1.00 X 3. X = [1.48 V E. X=D.29 Part B Which of the following best represents the location of the inection point of the function? V" A. :I: = U.12 X El. :I: : U.48 X C. X = [1.00 X D. X = [1.29 X E. X2048 For f (@) = sec , determine if the Intermediate Value Theorem applies on the interval [0, 4). If it does, find the value of c such that 0