The height of an object after t seconds is given by Ht9t227t

The height of an object after t seconds is given by H(t)=-9t^2+27t+2. Use calculus to determine the maximum height reached by the object.

Solution

H = -9t²+ 27t +2

For max height

dH / dt = 0

-9*2 t+27 =0

18t = 27

t = 3/2 sec

max height

h_max = -9*(3/2)² + 27 *3/2 +2

                = 22.25 units