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Problem 9 Easy Difficulty

Sketch the graph of a function $ f $ that is continuous on $ [1, 5] $ and has the given properties.

Absolute minimum at $ 3 $, absolute maximum at $ 4 $, local maximum at $ 2 $

Answer

Graph is shown in the video

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Video Transcript

We would like to sketch the graph of a function that is continuous and the closed interval 15. And that has an absolute minimum at three. An absolute maximum at four. And a local maximum up to. So we have from this craft which satisfies these all these requirements. First of all, the domain is The Interval 1 5. As we can see here And the even the function is continuous. There there is, there is only one piece of the function there. There are no jobs or discontinuities at whatsoever. I saw the first requirement is this and then let's see the other ones. The function has an absolute minimum at three as we can see here, the absolute minimum surround his mind that Sorry, it's around here is the lowest point in the graph in the whole domain, if we look at all the interval From 1 to 5. So At three we have the absolute minimum value and at four we have the absolute maximum and that's it at this point here for the anti highest Yeah, point in the graph if you look at the whole domain of the functions, so here we have an absolute maximum. Now, we have another requirement that we have a local maximum at two. And that's the case here, we can see it too. You have this point here which is the highest point when we look only close or near the value to. So if you look at a very small piece of the graph around this 0.2, we can see that it is the highest value there. So for that reason this is a local maximum value of the function. And then at one in five we have images that do not affect the three properties year. When we can see this solution to the problem, we have been given.

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