8. lff(x) = 1%, find PM and state the domains of both ftx) and f'(x). 9. Find the equation ofthe tangent line to the curve at the given point. fo) = (1,1) 1+:lc2 10. Find the equation of both tangent lines to the curve y = x3 - x that are parallel to the line 22): 2y + 1 = 0. 11. Suppose that f(2) = -3, f'(2) = 10, f'(4) = 6, 3(2) = 4, and g'(2) = 1. Evaluate 8) (MHZ) b) (f/gl'l2l Cl (\"#9) 12. If f(x) is a differentiable function, find an expression for PM in terms of f'(x). a) F(x) = f(x5) b) FCC) = [f(x)]5 13. If a ball is thrown downward from a 120 m high cliff with an initial speed of 18 m/s, then its height after t seconds, before it hits the ground is h = 120 18t 41-.9t2 3) Find the average velocity of the stone for the following time periods. i. 25tS3 ii. ZStSZJ iii. 2 S t S 2.01 b) Find the velocity at 2 seconds. c) Find the acceleration at 2 seconds. 14. The motion of a particle is described by the position function s=t36t2+9t+5,t2 0 where s is measured in meters and t in seconds. a) Find the velocity after 2 s and 4 s. b) Find the acceleration after 2 s and 4 s. c) When is the particle at rest? d) When is the velocity positive and when is it negative? e) When is the acceleration positive and when is it negative? f) Find the total distance travelled in the first 5 s