Which of the following corresponds to the derivative of f (@) = x* + 3x + 1 at x = 2? O A. f' (2) = lim h2 -Th h-0 h O B. f' (2) = lim h347h h O C. f' (2) = lim h 47h 411 h +0 h O D. f' (2) = lim 2h347h h O E. f' (2) = lim h +0 hUse the graph to answer the question. Which of the graphs below corresponds to the derivative of the function shown above? \fC. X D. XE. XGiven a function f (@) where f'(2) = 2, what is the equation of the line normal to the graph of the function at the point (2, 2)? O A. y = -2x + 6 O B. y = - c +3 O c. y= O D. y= 2 O E. y = 2x - 2A particle is moving along the x-axis. Which of the following statements is true if the particle is moving to the left and its speed is decreasing? O A. Its velocity is negative and its acceleration is negative. O B. Its velocity is positive and its acceleration is negative. O C. Its velocity is negative and its acceleration is positive. O D. Its velocity is positive and its acceleration is positive. O E. Its velocity is negative and its acceleration is zero.The function f (@) = is NOT differentiable over which of the following intervals? 124 51-6 O A. -2.5 2 O A. a = 2, b = 2 O B. a = 2, b = 0 O C. a= 3,b= -2 O D. a = 4, b = 0 O E. a = 4,b = -4Given the function f (@) = 2" which of the following best represents the value of the numerical derivative f' (5), determined using the symmetric difference quotient with h = 0.5? O A. 22.181 O B. 22.198 O C. 22.627 O D. 26.510 O E. 30.000Given that f (x) = 12-1 what is f' (x)? O A. f' (x) = (12 1)2 O B. f' (x) = (2_1)2 O C. f' (x) = -21 (12 1)2 O D. f' (x) = (12 1)2 O E. f' (x) =Given that f (x) = 2 41 what is f" (x)? O A. f" (x) = I O B. f" (@) = -3 O C F" (x) = O D. f" (*) = O E. f" (x) = 1What is the equation of the line tangent to the graph of the function f (@) = x - 7x + 3x + 1 at the point (1, -2)? O A. y= -8x + 6 O B. y = - 15 00 | H 8 o c. y=-2 O D. y = 17 8 O E. y= 8x - 10The volume of a cone is V= 3,". Suppose the height of the cone h is always 3 times the radius of the base r. What is the instantaneous rate of change of the volume of the cone with respect to the radius of the base? O A. dv O B. AP dr O c. dv dr O D. dv dr = 3mr O E. dV = 3mr2Suppose the position x of an object varies with time & according to the function > = 9t + 4t- , where x is in meters and t is in seconds. What is the speed of the object at t = 2 s? O A. 13 m/s O B. 16 m/s O C. 17 m/s O D. 25 m/s O E. 27 m/sThe height of a ball thrown vertically is given by the function h (t) = 6 + 10t - 16t , where h is in feet and t is in seconds. What is the ball's speed when it lands on the ground (h = 0)? O A. V = 6 ft./s O B. V = 22 ft./s O C. V = 26 ft./s O D. V = 32 ft./s O E. V = 42 ft./sWhich of the following best represents the slope of the line tangent to the graph of the function f (x) = 2x cos x at x = 0.5? O A. -0.96 O B. -0.48 O C. 1.28 O D. 1.76 O E. 2.23The position of an object bobbing up and down on a spring is given by the function s = 3 cost, where s is in inches and f is in seconds. Which of the following is the object's acceleration at t = 3 seconds? O A. -2. 97 in./$2 O B. -0. 42 in./$2 O C. 0 in./$2 O D. O. 42 in./$2 O E. 2. 97 in./ $2