Problem 1. {1 point) Let 32(1) 2 2 2x3, h'(2) : Use this to nd the equation of the tangent line to the curve y : 2 2x3 at the point (2, 14) and write your answer in the form: y = mx +1), where m is the slope and b is the y-intercept. Problem 2. {1 point) If a ball is thrown straight up into the air with an initial velocity of 40 ftls, its height in feet after: seconds is given by y = 401' 16:2. Find the average velocity for the time period begining when t = 2 and lasting (i) 0. 1 seconds (ii) 0.01 seconds (iii) 0.001 seconds Finally based on the above results, guess what the instantaneous velocity of the ball is when t = 2. Problem 3. {1 point) Find an equation of the tangent line to the curve y = ,7 7 2x 7 33:2 at (1,12). y: Problem 4. (1 point) If x) 2 x2 8.r 16, nd f'(a). Answer: Problem 5. (1 point.) xsin i if x y 0 L t : I . 6 x) {0 if x = 0 Determine whether or not f'(0] exists. Answer Yes or No: [WYes/No] Problem 6. (1 point) lff(x) : {2.1431111 ; if x 7 0 exists. . determine whether or not f' (0) 0 if x = 0 Answer Yes or No: ['?/Yes/No] Problem 7. (1 point) The limit . 1/49 + h 7 11m 5-10 h is the standard expression dening the derivative of some function f (x) at some number (I. Find f and a. f (x) = a = Problem 8. (1 point) The limit 2 lim (6 + h) 36 PlI-O h is the standard expression dening the derivative of some function f (x) at some number (I. Find f and a. f (x) = (I