After finding the critical points of the function, how do you find the global maximum and minimum. Is the most efficient way to simply find the value of the function at each of the critical points and the end points. This seems a little tedious. Is there a better way?
For example, say I know that on the interval (0,10), the critical points of f occur at x=1,5,6,8. To find the global maximum on [0,10], do I have to see which of f(0), f(1), f(5), f(6), f(8), and f(10) is the largest? There has to be a better way, isn't there?