Which of the following corresponds to the derivative of f (@) = x*+ 3x + 1 at x = 2? O A. f' (2) = lim h2-7h h-+0 h O B. f' (2) = lim h2+7h h-+0 h O C. f' (2) = lim h247h+11 h-+0 h O D. f' (2) = lim 2h247h h-+0 h O E. f' (2) = lim 7hath h-0 hUse the graph to answer the question. X Which of the graphs below corresponds to the derivative of the function shown above?O E.Given a function f (x) 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 = - 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 (@) = 12451-6 is NOT differentiable over which of the following intervals? 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. 30.000What is the equation of the line tangent to the graph of the function f (x) = x - 7x2 + 3x + 1 at the point (1, -2)? O A. y= -8x + 6 O B. y = - 15 8 O c. y= -2 O D. y = 17 8 O E. y= 8x - 103 The volume of a cone is V = #12 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. AP dr O B. dV dr O C. dV O D. dV dr = 3TT O E. dV dr = 3772Suppose the position x of an object varies with time t according to the function x = 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 his 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 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 clown on a spring is given by the function e = 3 cost, where s is in inches and t is in seconds. Which of the following is the object's acceleration at t = 3 seconds? 0 A. 4.9mm o e. 0.42in.,15-3 O C. Gill-{52 o o. 0.42 miss 0 E. 2. 97 mfg2