1.

Which of the following corresponds to the derivative of f (x) = 7 ng 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 16(14h) O B. f' (2) = lim ho L8(2 h) O C. f' (2) = lim h +0 [ 8(2 4 h) O D. f' (2) = lim 4(4 h) O E. f' (2) = lim h 0 4(4h)]Which of the following corresponds to the derivative of f (x) = 1 at x = 2, using the alternate definition of a derivative, reduced to its simplest form before taking the limit? O A. f' (2) = lim O B. f' (2) = lim 412 O C. f' (2) = lim -1 16(x-1) O D. f' (2) = lim -1 4(142) O E. f' (2) = lim 2(46)Which of the following graphs corresponds to the derivative of the function shown below? J" lGiven a function f {I} 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=2.'n+3 O B. y=%3 ar - 6x, x 1 If f (x) = , find the values of a and b that will make f (@ ) differentiable at x = 1. br? + 2, x >1 O A. a = 14, b =6 O B. a = 22 b = 18 5 5 O c. a = -10,b = -18 O D. a = -8,b = -16 O E. a = 2, b =0(0, ) except at which The function f (@) = cos (2)| is differentiable everywhere on the interval value of x? O A. I= O B. I= O C. = O D. I = O E. 1121-1 - V5 1 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 (x) = =41? 2:1. O A. f' (x) = O B. f' (x) = 212 O C. f' (x) = 212 O D. f' (x) = O E. f' (x) = 21 -1 212Which of the following is the second derivative of the function f (@) = .3 O A. f" (x) = 3r O B. f" (x) = 313 O C. f" (x) = O D. f" (z) = 201 42 O E f" (x) = 313What 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 = 2gy, 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 dy 2gy O B. ds 1 dy gy O C. ds dy 2y O D. ds dy O E. ds dy yThe location of an object moving along the x-axis is given by the function x = 10t + 5t - 0.8t 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 = 10.0The 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 speed decreasing? O A. when the velocity is negative and decreasing O B. when the velocity is positive and increasing O C. when the velocity is negative and the acceleration is negative O D. when the velocity is negative and the acceleration is positive O E. when the velocity is negative and the acceleration is zeroWhich of the following is the derivative of the function f (x) = sinc . (1 - cosc)? O A. f' (x) = cosx . sin r O B. f' (x) = - cost . sinT o c. f' (x) = cosx + cost . sinc O D. f' (x) = cost - cos r - sin c O E. f' (x) = cosx - cos'x + sincThe height of an object dropped from a 144-foot-tall building is given by the function s = -16t- + 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 = 5 2 sin t. Which of the following is the object's jerk at time t = $12 '3 A. 1 D 3. 0 C. U o o. J37 Which value of x in the interval > 1 (22 + 2)Find the equation of the line tangent to the curve defined by f (@) = at the point (1, 2). Show all your work. If limit notation is needed in your response, use the following example as a guide: lim (@* + 2 ) should : 1 be written as lim > > 1 (x2 + 2).The location x of a car in meters is given by the function = 30t - 5t , where t is in seconds. At the time when the car is moving at 10 m/s in the direction opposite to its initial motion, how far is the car from where it was at t = 0? Show all your work. If limit notation is needed in your response, use the following example as a guide: lim (a + 2) should be written as lim x -> 1 (22 + 2).The instantaneous rate of change of the volume V of a sphere with respect to its radius / can be expressed as dv dr a-. What is a? Recall that the volume formula for a sphere is V = = 17 Show all your work. If limit notation is needed in your response, use the following example as a guide: lim (2 + 2) should be written as lim ~ ~> 1 (x2 + 2).What is f" , where f (@) = sinc + cost? Show all your work. Write your final answer in simplest radical form. If limit notation is needed in your response, use the following example as a guide: lim (2 + 2) should be written as lim > > 1 (2 + 2)