Can you help me solve this problem please

Question

A man launches a toy rocket form the roof of a building 72 feet off the ground, the rocket has an initial velocity of 88 feet per second. The height of the ball t seconds after it was thrown into the air can be modeled by the function.

H(t)=-16t^2+88t+72

Find the maximum height that the ball reaches during its flight.

Answer 1

h(t) = -16t^2 +88t + 72

h'(t) = -32t + 88 = 0

t = 88/32 = 11/4 = 2 3/4 seconds to reach max height

h(11/4) = -16(11/4)^2 + 88(11/4) + 72 = -121 + 242 +72 = 193 feet = max height