Verify that the function is continuous on the interval [a,b].
Find all critical points of f(x) that are in the interval [a,b]. This makes sense if you think about it. Since we are only interested in what the function is doing in this interval we don’t care about critical points that fall outside the interval.
Evaluate the function at the critical points found in step 1 and the end points.
Identify the absolute extrema.