How do you use the Extreme Value Theorem to determine the global extrema of the function #f(x)=5+ (x^2)/(x+2)# on the closed interval [-1,3]?
Use what some authors call the Closed Interval Method.
The Extreme Value Theorem does not really tell us how to find extrema, it only guarantees that for a function that is continuous on a closed interval, there are extrema.
Nevertheless, we can find the extrema.
They must occur at either a critical number (in the interval) or at an endpoint of the interval.
So the method is: find critical number in the interval, then evaluate
The only critical number in the interval is
The maximum is
The minimum is