Which of the following corresponds to the derivative of f (x) = 12 at x = 2, using the primary definition of a derivative, reduced to its simplest form before taking the limit? O A. f' (2) = lim -1 h +0 [ 16(1+h) O B. f' (2) = lim 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 -1 h 0 [4(4th)Which of the following corresponds to the derivative of f (@) = at x = 2, using the alternate definition of a derivative, reduced to its simplest form before taking the limit? O A. f' (2) = lim I-+2 O B. f' (2) = lim I +2 O C. f' (2) = lim -1 1 +2 [ 16(x-1) O D. f' (2) = lim I-+2 4(1+2) O E. f' (2) = lim -1 1 +2 2(x+6)Which of the following graphs corresponds to the derivative of the function shown below?Given a function f (at) where 3\" (2) : % what is the equation of the line normal to the graph of the function at the point (2, 1)'? O A. y22ml3 D By: 0 E. yzmo ar3 - 6x, x1 O A. a = 14, b =6 O B. a= 22 b = 18 5 O C. a = -10,b= -18 O D. a= -8,b = -16 O E. a = 2, b=0The function f () = |cos (x ) | is differentiable everywhere on the interval (0, except at which value of x? O A. T= O B. T= O CE= O D. = O E. 12x-1| - V5-I Over which of the following intervals is the function f (@ ) = differentiable? COS O A. O B. (-2, 0) O C. 6 ' O D. (1, 4) O E. (4, 6)Given the function f (@) = =, which of the following best represents the value of the numerical 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. -1.000What is the derivative of the function f (@) = O A. f' (x) = 472 O B. f' (a) = 212 O C. f' (x) = T-+1 212 O D. f' (x) = 4x2 O E. f' (x) = 212-1 212Which of the following is the second derivative of the function f (x) = O A. f" (x) = 3.1.2 O B. f" (x) = 21 +2 3.13 O C. f" (x) = 4x +1 312 O D. f" (z) = O E. f" (a) = 2p3- 323What is the equation of the line tangent to the graph of the function f (x) = = + 2x - 5 at the point (2, 3)? O A. y = 2x - 1 O B. y = 3x - 3 O C. y= 4x -5 O D. y= 5x - 7 O E. y = 6x - 9The speed s of an object dropped from rest varies with the distance y it has fallen according to the equation s = V2gy, where g is the acceleration due to gravity. What is the instantaneous rate of change of the speed with respect to distance? O A. ds 1 dy 2gy O B. ds dy gy O C. ds 9 dy O D. ds dy O E. ds dyThe location of an object moving along the jaraxis is given by the function :1: : lt + 5t? H.8t3. At what positive time does the object stop moving? O A. t=.8 O E. tz'i C} C. t=32 O D. t=5 O E. t: 'i The height of an object thrown vertically upward is given by the function s = -4.9t + 20t + 2, where s is in meters and t is in seconds. What is the object's velocity at t = 3 seconds? O A. -5.3 m/s O B. 5.3 m/s O C. -9.4 m/s O D. 9.4 m/s O E. 17.9 m/sGiven a position function for an object: under which of these conditions is the object's soeed decreasing\"? O t. when the velocity,r is negative and decreasing O E. when the velocity,r is positive and increasing O [3. when the velocity,r is negative and the acceleration is negative O D. when the velocity,r is negative and the acceleration is positive O E. when the velocity,r is negative and the acceleration is zero Which of the following is the derivative of the function f (x) = sinc . (1 - cos x)? O A. f'(x) = cosx . sinc O B. f'(x) = - cosx . sin . o c. f' (x) = cosx + cosx . sin x O D. f' (x) = cosx - cos- x - sin' x O E. f'(x) = cosx - cos'x + sin'xThe height of an object dropped from a 144-foot-tall building is given by the function s = -16t2 + 144, where s is in feet and t is in seconds. Find the object's speed when it hits the ground. O A. -96 ft./s O B. -32 ft./s O C. Oft./ s O D. 32 ft./s O E. 96 ft. / sThe position of an object is given by the expression 3 = E: 2 sin t. WhiCh of the following is the object's jerk ettimet: $3 O A. 1 o E. _ O o. o o D. vs Which value of x in the interval