1. Match graphs 3, b, and c of y 2 x} with their corresponding derivatives, graphs A, B, and C. Give reasons for your choice. a} ' A y 2 2 0 2 x 2 o 2 x 2 2 b) y B )' 2 2 / Z 0 2 x 2 d c-7r ~20 2. a} State the derivative of at} =x3. b) Evaluate each derivative. nfem wream iii} {(9 iv} 9%) 5. Each derivative represents the first princip definition for some function f(x). State the function. a) f'(x) = lim 3(x + h) - 3x b-0 b 4(x + b)3 -4x3 () f'(xc) = lim b-0 b 5 e) f'(x) = lim xth X b-0 b14. Use the first principles definition to determine dy for each function. dx a) y = 8x b) y= 3x2 - 2x () y= 7-x2 d) y = x(4x + 5) e) y = (2x - 1)216. The height of a soccer Reasoning and Proving ball after it is kicked Representing Selecting Tools into the air is given by Problem Solving H(t) = -4.91- + 3.5t+1, Connecting Reflecting where H is the height, in Communicating metres, and f is time, in seconds. a) Determine the rate of change of the height of the soccer ball at time t. b) Determine the rate of change of the height of the soccer ball at 0.5 s. c) When does the ball momentarily stop? What is the height of the ball at this time? 17. a) Use the first principles definition to dy determine for y = x2 - 2x. dx b) Sketch the function in part a) and its derivative. c) Determine the equation of the tangent to the function at x = - 3. d) Sketch the tangent on the graph of the function