Genesis kicks a football. Its height in feet is given by h(t)= -16t^2+48th(t)=−16t 2 +48t where tt represents the time in seconds after kick. What is the football’s greatest height?

The greatest height is 30 ft.

h = 48t - 16t^2

Differentiating, the rate of change of height dh/dt = 48 - 32t.

The football will be at rest when dh/ht = 0, that is, when 48 - 32t = 0, t = 48/32 = 3/2.

The height at that time will be 48*(3/2) - 16*(9/4) = 72 - 36 = 36 ft.