I really need help on these problems. I know it's a lot, but I can't split the question.

\fGiven that f [I] and its inverse, f '1 [3} are differentiable functions with f {z} and j" {at} values at x = :2 X = a and I = 4 as indicated in the table, nd the derivative at f4 (a) at x = 2. I\" \fFind the linearization L (@) of f (x) = (1 + x)" at x = 0, and use it to find an approximation of f (-0.2) O A. L (-0.2) = 0.2 O B. L (-0.2) = 0.4 O C. L (-0.2) = 1.8 O D. L (-0.2) = 3.8 O E. L (-0.2) = 4.2In (12 3) Create a table to develop an estimate of lim Which of the following best represents that limit? 2-I O A. -4 O B. -2 O C. O O D. 2 O E. 4\fWhat of the following best represents the left-end behavior model of the function f (x) _ 1 2 4-1 ? O A. g(x) = x- - 2x O B. g(x) = 12 - o c. g(x) =x2 O D. g(x) = x2+ O E. g(x) = x' + 2xWhat value of a Will make the following function continuous? 3:1,} {Em3,352 I = zoz+1, 2:2 0 A. 2 D E. 1 C) CC! C) I11 (12 4x 2) sin(1 For which of the following intervals does the function f (@) = have a removable 1 3r' | 21 discontinuity? O A. [-2.5, -1.5] O B. [-1.5, -0.5] C. [-0.5, 0.5] O D. [0.5, 1.5] O E. [1.5, 2.5]This question has two parts. First, answer Part A. Then, answer Part B. Part A You are given a continuous polynomial function f (@) with select values shown in the table. X f (x) -9 4 23 3 -1 2 What is the minimum number of values of x where f (x) = 0? O A. 2 O B. O O C. 1 O D. 3 O E. 4Part B For the same continuous polynomial function f {as} with select oerivative values shown in the table, what is the minimum number of values on where the slope of f [a] is zero? Cl AID Cl EL'1 D (3.2 D [1.3 Which of the following is NOT a valid definition of a derivative? O A. f' (a) = lim f(z)-f(a) O B. f' (a) = lim f(ath)-f(a h) h +0 2h o c. f' (x) = lim f(Ith) f(h) h +0 h O D. f' (x) = lim f(Ith)-f(I) h +0 h O E. f' (x) = lim f(eth) f(x h) h +0 2hWhich of the following corresponds to the derivative of f (@) = ces, using the primary definition of a derivative, reduced to its simplest form before taking the limit? O A. f' (x) = e lim -1 h +0 2h O B. f' (x) = xe lim h 0 2h o c. f' (x) = e lim h +0 O D. f' (x) = xef lim h >0 h O E. f' (x) = xe lim 2 h >0 hThe following table gives values [if i', j", g, and g" at selected values of X. If h [I] = f {y {33]} what is h' [1]? \fThis question has two parts. First, answer Part A. Then, answer Part B. Part A What is f' (x) given that f (x) = x Inx - x7 O A. f' (x) = 2xInc O B. f'(x) = latx-1 o c. f' (x) = 2xlnx-x - 1 O D. f' (x) = 2xInc+x-1 O E. f'(x) = 2xInx + 2x - 1 Part B What is f" (x)? O A. f" (x) = 2lnx+1 O B. f" (x) = 2Inx + 2 O c. f"(x) =21x + 3 O D. f" (x) = 2Inx + 2x+1 O E. f"(x) = 2Inx + 2x +3\fThis question has two parts. First. answer Part A. Then, answer Part E. Part A A polynomial function 131(3) has degree 3. 1What shape will 13' {3] have? 0 A. a straight line with a nonzero slope C! E. a horizontal line D C. a parabola C! D. a vertical line D E. cannot be determined Part B A polynomial function 131(3) has degree 3. 1What shape will 13'" {I} have? 0 A. a straight line with a nonzero slope C! E. a horizontal line D C. a parabola O D. a vertical line C! E. cannot be determined This question has two parts. First, answer Part A. Then, answer Part B. Part A Where does f (x) = + 3x- - 5x - 2 have a local maximum? O A r = 1+ 2v6 3 O B. = -1- 3 O C. I= -1+ 16 O D. 1= -1- 2V/6 3 O E x= -1+ 2v6 3 Part B What is the x-value of the inflection point of f (x)? O A. D= -1 O B. I= O C. X=0 O D. I= O E. x = 1This question has two parts. First, answer Part A. Then, answer Part B. Part A Suppose you are given the function f (@) = sinc + bcosx. Which of the following relationships will ensure that a local extremum occurs at x = k in the interval (0, ? )? O A. b= -2 cot k O B. b = - cot k O c. b = - tank O D. b = cot k O E. b = tank Part B Which of the following relationships will ensure that an inflection point occurs at x = k in the interval (0, #)? O A. b= -2 cot k O B. b = - cot k O c. b = - tank O D. b = cot k O E. b = tankThis question has two parts. First. answer Part A. Then, answer Part E. Part A Suppose you are given the function f [I] = .23"T Eek + 1. 1Which of the following best represents the location of the global minimum of the function? G A. a: = .43 0 El. .1: = 4.112 C! C. X= D D. 1:13.48 C) E. X=29 Part B Which of the following best represents the location of the inflection point of the function? G A. a: = .12 C! E. a: = .43 Cl C. x= D D. 1:13.29 C! E. X=.48 Suppose f (x) = x2 - 1 for x > 1. What values of a and b will ensure that f () is differentiable for all values of x? O A. a = b IT O B. a= - .b = O C. a= - b = O D. a = - b O E. a = , b =For f (x) = sec TL ", determine if the Intermediate Value Theorem applies on the interval 0, 4 . If it does, find the value of c such that 0 > 1 O E. There is no interval on which f (@ ) is concave up