# Find the absolute maximum and minimum of the function

## How do I find the absolute maximum and minimum of a function? In this section we discuss how to find the absolute (or global) minimum and maximum values of a function. In other words, we will be finding the.

Given a particular function, we are often interested in determining the largest and smallest values of the function. This information is important in creating accurate graphs. Finding the maximum and minimum values of a function also has practical significance because we can use this method to solve optimization problems, such as maximizing profit, minimizing the amount of material used in manufacturing an aluminum can, or finding the maximum height a rocket can reach. In this section, we look at how to use derivatives to find the largest and smallest values for a function. The function does not have an absolute maximum. First, the term absolute here does not refer to absolute value. An absolute extremum may be positive, negative, or zero.

On a closed interval, the extreme values of a function may happen at critical points or endpoints. We will find all critical points of the function, and then check the function's value at those points against the function's value at the endpoints. Become a Study. Try it risk-free for 30 days. Watch 5 minute video clips, get step by step explanations, take practice quizzes and tests to master any topic. I love the way expert tutors clearly explains the answers to my homework questions. Keep up the good work!

If the slope is zero, you know that there is a relative maximum or minimum. We need to check if it is the absolute maximum or minimum or not.
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To do this we will need many of the ideas that we looked at in the previous section. First, since we have a closed interval i. This is a good thing of course. Next, we saw in the previous section that absolute extrema can occur at endpoints or at relative extrema. Also, from the previous section that we know that the list of critical points is also a list of all possible relative extrema. So, the endpoints along with the list of all critical points will in fact be a list of all possible absolute extrema.

## 4.1: Maximum and Minimum Values

The end points could be the maximum or minimum because we don't know where the function starts or finishes. If the slope is zero, you know that there is a relative maximum or minimum. We need to check if it is the absolute maximum or minimum or not.

## 4.1: Maximum and Minimum Values

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Finding absolute extrema on a closed interval. Extreme value theorem tells us that a continuous function must obtain absolute minimum and maximum values on.