Question

A ball is thrown vertically into the air so that its height s after t seconds is given by the equation, s=-1/27(t^2)+4√t. Find its maximum height.

Answer 1

ds/dt = -2/27 t + 2/√t
= (54-2t^(3/2))/(27√t)

ds/dt=0 when

54 - 2t^(3/2) = 0
t^(3/2) = 27
t = 9

now just find s(9)