Which of the following corresponds to the derivative of f (@) = =+% at x = 2, using the primary definition of a derivative, reduced to its simplest form before taking the limit? O A. f' (2) = lim h +0 [ 16(1+h) O B. f' (2) = lim -1 h +0 8(2-h) O C. f' (2) = lim -1 h +0 [ 8(2+h) O D. f' (2) = lim -1 h +0 [4(4-h) O E. f' (2) = lim h +0 [4(4+h)Which of the following corresponds to the derivative of f (m) = 1 . 1\" at x = 2, usmg the alternate definition of a derivative, reduced to its simplest form before taking the limit? 0 A f'(2)= O :z:>2 .. l .1111 ] 81: Which of the following graphs corresponds to the derivative of the function shown below? y \fC. O D. XGiven a function m) where f' (2) = %, what is the equation of the line normal to the graph of the function at the point (2, 1)? O A. y=2m+3 O B.'y=$ ax - 6x, 251 If f (2 ) = (bx2 + 2, x>1 , find the values of a and b that will make f (@) differentiable at x = 1. O A. a = 14, b = 6 O B. a = 7, b= - 5 O C. a= -10, b = -18 O D. a= -8, b= -16 O E. a =2, b = 0The function f () = |cos (Tra) | is differentiable everywhere on the interval (0, 5 except at which value of x? O A. *= O B. C= O C. = O D. C= O E. 1l2:l| - vz Over which of the following intervals is the function f (2:) = differentiable? O B. (2,0) 0 0. (gig) O D. (1,4) Given the function f (m) 4 , which of the following best represents the value of the numerical _E derivative f' (2). determined using the symmetric difference quotient with h = 0.5? O A. 1.333 O B. 1.067 O C. 1.010 O D. 1.003 O E. 1.0(][) \f9+1 9 Which of the following is the second derivative of the function f (2:) = 3r . 2:3 0 A_ fr:($)=23121 1.3_ O 3- mm) = if 2:3 0 C. f\"($)= 43121 O D_ If\" (3) = 2033+; 3:1:2 0 E_ f\"($) = 2:c32 3:1:3 What is the equation of the line tangent to the graph of the function f (m) = $2 + 23 5 at the point (2, 3)? O A.y=231 O B.y=3m3 O C.y=4m5 O D.y=537 O E. y=639 The speed s of an object dropped from rest varies with the distance y it has fallen according to the equation 5 = 1 r 2 , where g is the acceleration due to gravity. What is the instantaneous rate of change of the speed with respect to distance? 0 A. E _ E E; _ 293; O B. E = i dy 93! O C. E _ i E; _ 3y 0 D. E = E dy 9' O E. d: 29' The location of an object moving along the x-axis is given by the function * = 10t + 5t2 - 0.83. At what positive time does the object stop moving? O A. t = 0.8 O B. t = 1.6 O C. t = 3.2 O D. t = 5.0 O E. t = 10.0