What is the maximum height obtained by the ball

an astronaut on the moon throws a baseball upwards. the height of the ball in feet is given by the equation y=-2.7t^2+30t+65, where t is the # of seconds after the ball was thrown.

a) at what time does the ball reach it's maximum height?

b) what is the maximum height obtained by the ball?

a)Rate of change = d(s)/d(t)
Differentiate: y’ = -5.4t+30
Stat. Points occur when y’ = 0

-5.4t = -30
5.4t = 30
t = 30/5.4
t = 5.6 seconds ( to 1. dp.)

b)-2.7(5.6)^2 +30(5.6)+65 = 148.3 (to 1 d.p.) feet

y= -2.7t^2+30t+65 at maximum height y, dy/dt=0
dy/dt = -5.4t +30 = 0 giving t=30/5.4=5.55 seconds
ball reaches maximum height 5.55 seconds after throwing.

using t =5.55, y=-2.7*(5.55)^2 + 30*5.55 + 65 =153.9 ft.