Use the following graphs to identify the points (if any) on th...

Question

Use the following graphs to identify the points (if any) on the interval [a, b] at which the function has an absolute maximum or an absolute minimum value

Accepted Answer

Hello, in this video, we are going to be identifying the X values where the absolute maximum or minimum is located at. The problem asks us to examine the function F of X plotted on the interval from 0 to 4. We want to identify the X values where the function attains its absolute maximum or minimum. So, what does it mean to have an absolute maximum or minimum? What this statement means is that we want to find the points of the graph that reaches the highest possible value or lowest possible value on the defined interval. Let's go ahead and start this problem by identifying the absolute minimum. Now, if we are taking a look at the given graph, what seems to be the lowest possible point that the graph reaches on the defined interval? While the lowest possible value is located at the bottom of this valley. At this point, we can approximate that Y is approximately negative 0.25. So this is the lowest possible Y value that the graph ever reaches. And this point is roughly located at X is equal to 1.5. So what this means is that we can identify the X value of the absolute minimum to be X is equal to 1.5, and this is going to be the first solution to this problem. Now, what about the other half? What about the absolute maximum? If we are taking a look at the graph, what seems to be the highest possible value that the graph reaches on the defined interval? Well, that value seems to be located here, with the respective Y value, Y is equal to 6. At this point, the respective X value is going to be X is equal to 4. Now we could say that the absolute maximum is going to be located at X is equal to 4, but we need to be careful. Notice that this endpoint is represented with an open circle. What this means is that this value is not included in our defined interval, and with that being said, that means that even though this is the highest point that the graph reaches, since this value is not included, that means we do not have an absolute maximum value, so there is no absolute max. And that is going to be the 2nd solution to this problem. So I hope this video helps you in identifying the absolute maximum and minimum, and I will go ahead and see you all in the next video.

Use the following graphs to identify the points (if any) on the interval [a, b] at which the function has an absolute maximum or an absolute minimum value <IMAGE>

Key Concepts

Absolute Maximum and Minimum

Critical Points

Evaluating Functions on an Interval

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