Maxima and minima on a CLOSED interval (KristaKingMath)

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The process for finding the extrema on a closed interval is the same as the process for finding extrema on an open interval. You'll take the derivative of the function, and then set the derivative equal to 0 to solve for critical points.
Because you're looking at a closed interval, you should only consider the critical points within the interval. Any critical points outside the interval can be ignored.
Then you'll use the first derivative test to characterize the critical points inside the interval, and both endpoints of the interval. Because the interval is closed, you can call the critical point or endpoint with the highest value the global maximum, and you can call the critical point or endpoint with the lowest value the global minimum. All other critical points or endpoints will be called local maxima and local minima, which of course will be the local extrema of the function on the closed interval.
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