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For the graph ofy = f(x) shown to the right; find the absolute minimum and the absolute maximum over the interval [1,12].IaenIty Ine apsolute minimum beiecI Ine cor...

Question

For the graph ofy = f(x) shown to the right; find the absolute minimum and the absolute maximum over the interval [1,12].IaenIty Ine apsolute minimum beiecI Ine correct cnoice peiow TIII in any answer poxes wiInin your cnoice.A The absolute minimum is at X= and x= (Round to the nearest integer as needed. Use ascending order:)B. The absolute minimum is at X= (Round to the nearest integer as needed:) 0c. There is no absolute minimum.Identify the absolute maximum. Select the correct choice below fi

For the graph ofy = f(x) shown to the right; find the absolute minimum and the absolute maximum over the interval [1,12]. IaenIty Ine apsolute minimum beiecI Ine correct cnoice peiow TIII in any answer poxes wiInin your cnoice. A The absolute minimum is at X= and x= (Round to the nearest integer as needed. Use ascending order:) B. The absolute minimum is at X= (Round to the nearest integer as needed:) 0c. There is no absolute minimum. Identify the absolute maximum. Select the correct choice below fill in any answer boxes within your choice_ 0A The absolute maximum is atx= and x= (Round to the nearest integer as needed. Use ascending order:) 0 B. The absolute maximum is at X= (Round to the nearest integer as needed:) 0c: There is no absolute maximum:



Answers

For graph of a function $y=f(x),$ find the absolute maximum and the absolute minimum, if they exist. Identify any local maximum values or local minimum values.
(Check your book for graph)

We are going to discover the absolute extremely here and along the way. We also are going to state where are local extreme are this point here? The point of 11 would be a local minimum because the slope is going from a negative slope to a positive slope. There is also a local maximum here because the slope is going from a positive to a negative slope. Now it's possible that those local extreme it could also be absolute extreme. A. The local maximum is actually also an absolute maximum because the largest function value is four, so there is an absolute maximum at the 0.44 But the local extreme of 11 is not the absolute minimum because the function value actually drops all the way down to zero. So are absolute. Minimum value is zero, and that absolute minimum occurs at the point of five zero

There are two local extreme A in this graph. At the point of 11 we can see the slow ghosts from negative to positive, so there is a local minimum at the point of 11 There's also a local maximum because of slow goes from positive to negative, and that is that for four now, in terms of the absolute extreme, a. The function value of four is also the largest function value, so that local max is also the absolute max. Absolute maximum occurs of the point of 44 The absolute minimum is also at the local minimum because that's a smallest function value we have, so there is an absolute minimum that will occur at the point of one one.

We are looking in the scrap to see where we have absolute extreme and we're also going toe list where the relative extreme are as well Well, if we look at where there's a direction change, there does happen to be a direction changed when X is, too. However, that's, Ah, hollow point. So normally that would be a relative max. But in this case, since that point doesn't actually exist, there is no relative Max. There also is no relative minimum because there's no point where it changes from a negative slope to a positive slope. So we'll say there are no local extreme. What about the absolute minimum? A Max? There is an absolute minimum right here because the smallest function value plotted is once will say, there is an absolute minimum at the point of 01 Now, for the absolute maximum, we can see that it's getting very close to four but never quite reaches for well, there is no one single number that's closest of four for any number we give, like maybe 3.99 We could always make one closer like 3.999 Therefore, there is no absolute extreme during no absolute maximum

First, let's look for the local extreme. A. There are three points where there are direction changes the X value of zero. It goes from a negative slope to a positive slope, so there is a local minimum at the 0.0 There is a local maximum when X is, too, because there is changing from a positive slope to a negative. So we put local max aunt 23 And then there's another local minimum at 32 because it's changing from negative slope to a positive. Now for the absolute extreme, A. The absolutely smallest function value is zero. So we will put absolute minimum will occur at the point of 00 What about the absolute maximum? This part of the graph here is just going to keep going up and up. So the Y value is gonna be increasing without bound. So there is no absolute maximum


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