Question is below in the description

Question

The ball was caught by a fan, sitting in the first row of the seats above the Green Monster. The fan threw the ball straight up into the night sky. As the ball came down, it was caught 6 feet above the ground by the left fielder who was standing at the base of the wall.

From the time the ball was initially thrown by the fan until the time it landed in the glove of the left fielder, the height of the ball above the ground is given by the formula:

y=h(x)=37+88x-16x²

where x denotes time in seconds and h(x) denotes height in feet.

1. From the time the fan threw the ball, how long did it take for the ball to land in this left fielders glove?
2. What is the maximum height attained by the ball?
3. what was the velocity of the ball in feet per second when it high the left fielder's glove?
4. What should you take for the domain of this function?

Answer 1

1. When x is the solution of h(x)=6
2. When x=11/4, i.e. when the derivative = 0, or at 32x=88.
3. Find the derivative of h(x) and evaluate it at the time determined in the first answer.
4. The domain is the closed interval from 0 to the time determined in the first answer.