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Homework #6 Math 180 Name: Determine the anti derivative of the following functions: A f(x)=(3x+2) (5x-2)(3* +1) b)) (x)= (2% 45 (Vo +5x) 9 f(x):18\\/x_9f/\\xzx+27 d) f(x): sin(x) 27 15sec2(x)3x+4 9 fl)=Vx- +e" 5secxtanxcsc'x+4 4 V1= x? Determine the function f(x) given the following: a) f"(x)=x"+3cosx; (0)=2; /'(0)=3 by f)=12x-4; f(2)=8 f(-1)=6 c) f'(x)=2sin(x)-x+1 '(0)=2and (0)=-1 a) Given the marginal cost of c'(x) =3x" 4x+5, where C is in dollars, x units of items and a cost of $1,000 for producing 10 items, find the cost function. b) A ball is thrown upward with an initial velocity of 14.7 m/s from the edge of a platform 19.6 m above ground level. i) Find the position function and calculate the displacement of the ball at t = 3s and t = 3.5s. i) Find the highest point the ball can reach and impact speed when it strkes the ground. c) A bus accelerates uniformly at 1.8 m/s> cruises at 12 m/s, and decelerates uniformly at 3 m/s?> when braking. Calculate the trip time between two stops 500 m apart. d) The driver of a fast car traveling on a narrow road at 40 m/s sees a slow bus 300 m ahead traveling at 10 m/s in the same direction. What constant decelerate braking capability does the car need to avoid the collision if the us continues with constant velocity? e) You are driving along a highway at a steady 60 mph (88 ft/sec) when you see an accident ahead and slam on the breaks. What constant deceleration is required to stop your car in 242 ft