The profit function for good x is given by P(q) = 200 + 1009 + 30q²-9² where q is the quantity of x sold. (a) Determine the value of q resulting in the largest profit. (b) Calculate the maximum profit. Why might the profit be lower if q is higher than this?

You throw a bowling ball vertically with an initial velocity of 25 meters per second. The height of this bowling ball in meters with time measured in seconds is modeled by the function H₁ (t) = -5t² + 25t. You wait one second and then throw another ball vertically with initial velocity 30 meters per second. Its height is modeled by H₂(t) = -5(t− 1)² + 30(t-1). At what time (if any) will the two balls collide? How high are the balls when they collide?