Find the derivative.
Set this equal to 0. Solve and only keep values that are contained in [3,10].
But that's not all.
At the endpoints of the interval, you need to figure out if they are 'maximums' or 'minimums' and by that I don't mean they are stationary points.
See the function of I have attached. At the endpoints (which are indicated by the vertical black lines) we have a 'maximum' at the right hand one (near x=5) and a 'minimum' at the left hand one (near x=-5).
These are only maxs and mins on the interval.