Question

A spot of light is made to travel across a computer screen in a straight line so that, a t seconds after starting, it's distance from the left hand edge (d cm) is given by the function d(t) =7t - t² +2. Find the furthest distance the spot light travels and how long it takes to travel this distance.

Answer 1

so you just want the max of d(t)

find the derivative, set it equal to zero, and solve that for t

Once you have the value of t which gives you the maximum, plug it back into d(t) to actually find that distance.
Very straight-forward.