Section 4.9 - Antiderivatives 1. Find the most general antiderivative of each function below: (a) f(x) =2vx+6cosx ( b ) f (x ) = 2+x2 1+ x2 2. Find the antiderivative F off which satisfies the given condition: f(x) =4-3(1+x) , F(1) =0. 3. Find y = f(x) such that dy dx2 = 2e* +3sin x with f(0) =0 and f(x) = 04. A particle moves with acceleration function a(t) = 5 +41: 2t2. Its initial velocity is v(0) = 3 mfs and its initial displacement is 5(0) = 10 m. Find its position after t seconds. 5. A car is traveling at 50 mph when the brakes are fully applied, producing a constant deceleration of 22 it's2 . What is the distance traveled before the car comes to a stop? 6. Two balls are thrown upward from the edge of a cliff which is 432 ft above the ground. The rst ball is thrown with a speed of 48 fs and the second ball is thrown with a speed of 24 fs. Do the balls ever pass each other