Given equation is
We have to find the time interval by which height is maximum.
We start with differentiating .
Differentiating h(t) ,
Differentiating again
Since on double differentiating , we are getting a negative number, so the height is maximum.
And to find the time of maximum height, we set h'(t) to 0, that is
In second part, the height is decreasing means slope, h'(t) is less than 0. That is,
So the required time interval is