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Determine from the graph whether the function has any absolute extreme values on $[a, b] .$ Then explain how your answer is consistent with Theorem 1GRAPH CANT COPY...

Question

Determine from the graph whether the function has any absolute extreme values on $[a, b] .$ Then explain how your answer is consistent with Theorem 1GRAPH CANT COPY

Determine from the graph whether the function has any absolute extreme values on $[a, b] .$ Then explain how your answer is consistent with Theorem 1 GRAPH CANT COPY



Answers

Determine from the graph whether the function has any absolute extreme values on $[a, b] .$ Then explain how your answer is consistent with Theorem 1 GRAPH CANT COPY

In this problem, we're given a function are actually we're gonna grab function. And as you can see, we have this empty circles so left and right spends. Maybe. So this is a grand off F in an open Peter. So this sell this wanting this purse tells us that we cannot apply 01 So they're one does not a lie. Additionally, we can see from a scrap that we have an absolute maximum with this porn. Absolutely. However, the graft might say sharp turn right here. So this implies discontinuity. So the function is that protein. It's up the sport again. Um, it means that we cannot apply it. Karen. So they're not continuous. This all seems implies that someone

Okay, so we see from the scrap, um, that Michael's FX has and Absolute Max at X equal. See the highest point on the graph and it's obtained by the function. And we have an absolute men at X equals being, And this is consistent with the extreme dying there because this is a continuous function on a closed interval. So therefore, it must have been upset Maxim absolute mitt, and we could see right where those are.

Dysfunction actually has an absolute maximum in absolute minimum. So if you look over, eh? Here's our function. Kind of that a seeing being so a even though it's not continuous today, um, this value here is the largest value, and all other numbers of function takes on for smaller than this about as similarly, This is the absolute minimum X equal. See, because this value is smaller than all other values the function takes on. So here we have an absolute max and C, we have an absolute man.

Okay, so this function each of X has no absolute maximum or absolute minimum. And the reason is Okay, so you possibly might say that an X equals a. That's an absolute maximum. But the problem is at X equals a. The function is approaching a value but never actually reaches that. So the maximum is never attained. It's very important that for function to have an absolute maximum or minimum that the function actually attain that value in the same thing is true for sea. It may look like sea is an absolute minimum, but there's value that we're approaching from the left and the right. The function never obtains that value that scene. And so the dysfunction has no absolute expended upset minima. And this doesn't contradicts the extreme value there. For two reasons. It's not continuous, and it's also not to find card enclosed interval. And so, in order to have enough setbacks, my hand and absent minima, we need to continue this function to find on the closed a little


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