3) Differentiate the following functions. [K] a) y = 6x4 - 5x3 + 3x by = (7x + Vx2+ 3) c) y = (3x2) (Vx) d) y = x (cosx) e) y= 3x-2 V1-x f) y = In (5x2 + 9) 3 3\fn) y = 3x2 (x3 + 1)7 o) y = e2x + e3 p) y = x 5 - V5x q y= r) y = sin*x s) y = = In x 4) A construction worker accidently drops a hammer from a height of 90 m while working on the roof of a new apartment building. The height, s, in meters, of the hammer after t seconds can be modelled by the function s(t) = 90 - 4.9 t2, t2 0. [A] a) Determine the average velocity of the hammer between 1 s and 4 s.b) Determine the velocity of the hammer at 1 s and 4 s. c) When will the hammer hit the ground? d) Determine the acceleration function. 5) Consider the vectors u = [8, -5, 4], v = [1, -3, -2] and w = [3, 7, 0]. [C] a) Evaluate the expression u x v . w 6b) Determine the projection and its magnitude of u on w. c) Determine the angle between u and v. 6) For the function f (x) = x3 + 6x2 +9x : [K] Determine the domain of the function Determine the intercepts of the function iii ) Determine and classify the critical points of the function iv) Determine the points of inflection Determine increasing and decreasing intervals vi) Sketch the graph of the function 77) Draw the resultant vector at + B and determine the magnitude and direction of the vector relative to the x-axis. [T] 8) Without solving mathematically, explain how you would find the 75th derivative of the equation y = cosx. [C] 9) Justin applies a force at 20 to the horizontal to move a football tackling dummy 8 m horizontally. He does 150 J of mechanical work. What is the magnitude of force? [A]