The position of a particle moving along the x axis depends on the time according to the equation

[@samatronic123]

why do we have to find the derivative to find the max X position?

[@monkeyslayer2183]

Because a derivative can show you the maxes and mins. In a derivative when you derive a function any change in sign (so going from positive decreasing to negative increasing) can be shown as a maximum. So to find the max, you derive it.

[@IshaShah-hd5tt]

Because at maximum height velocity is zera