Finding Absolute Extrema of f(x) on [a,b]
0. Confirm that the function is continuous on the interval [a,b].
1. Determine all critical points of f(x) which are in the interval [a,b]. it makes sense if you think about it. As we are only interested in what the function is doing within this interval we don't care about critical points which fall outside the interval.
2. At the critical points evaluate the function found in step 1 and the end points.
3. recognizes the absolute extrema.
There actually isn't a whole lot to this procedure. We called the first step in the procedure step 0, mostly since all of the functions which we're going to look at here are going to be continuous, although it is something that we do have to be careful with. This procedure will only work if we contain a function which is continuous on the given interval. The most labor intensive step of this procedure is the second step (step 1) where we determine the critical points. This is also important to note that all we desire are the critical points which are in the interval.