Question

Sam hits a golf ball from a elevated tee

Answer 1

First take a derivative,

`(d)/(dx)-5t^2+10t+30=-10t+10=-10(t-1)`

Now compute the critical point where the slope is 0,

`-10(t-1)=0\implies t-1=0\implies t=1`

And done.

The maximum height is at
`t=1` of
`h(1)=-5+10+30=35`.

Hope this helps :)