The height in feet of a water rocket launched from the groun

The height in feet of a water rocket launched from the ground is given by the function h(t) = -16t^2 + 96t where t represents the number of seconds after launch. What is the max height attained by the rocket?

Solution

To find max height , h(t) must be maximum.

To find maximum of function the derivative of that function must be zero i.e. h\'(t) = 0

h\'(t) = 0

or, -16 * 2 * t + 96 = .

or, 32t = 96

or, t = 3

at , t = 3, h(3) = -16 * 3² + 96 * 3

                      = 144

Maximum height obtained by the rocket is 144