for-graph-of-a-function-yfx-find-the-absolute-maximum-and-the-absolute-minimum-if-they-exist-ident-2

Name: for graph of a function yfx find the absolute maximum and the absolute minimum if they exist ident 2
Uploaded: 2020-07-06
Duration: 1 min 21 s
Channel: Numerade
Description: 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)

Question

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)

Jonathon Brumley · Accepted Answer

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&#x27;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

Jonathon Brumley · Answer

we&#x27;re going to determine the absolute extreme a and along the way. We also are going to identify local extreme A. There do happen to be to local minimum a maximum values. There is a local maximum value right here because there&#x27;s a direction change where it&#x27;s going from a positive slope toe a negative slope. There is a local max at the point of 33 There&#x27;s also a local minimum here at the point of to to. Sometimes those local extreme are also absolute extreme. But the absolutely largest function values right here. So the absolute maximum is the function value of four, and that would exist to the point of 14 The absolute minimum would be here because that&#x27;s the smallest function value I get. So there is an absolute minimum value of one, and that occurs at the point of five one

Jonathon Brumley · Answer

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&#x27;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&#x27;s a smallest function value we have, so there is an absolute minimum that will occur at the point of one one.

Jonathon Brumley · Answer

We are looking in the scrap to see where we have absolute extreme and we&#x27;re also going toe list where the relative extreme are as well Well, if we look at where there&#x27;s a direction change, there does happen to be a direction changed when X is, too. However, that&#x27;s, Ah, hollow point. So normally that would be a relative max. But in this case, since that point doesn&#x27;t actually exist, there is no relative Max. There also is no relative minimum because there&#x27;s no point where it changes from a negative slope to a positive slope. So we&#x27;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&#x27;s getting very close to four but never quite reaches for well, there is no one single number that&#x27;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

Jonathon Brumley · Answer

first, let&#x27;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&#x27;s another local minimum at 32 because it&#x27;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

Jonathon Brumley · Answer

there is one relative or local minimum and one relative or local maximum. There is a relative minimum here because it changes from a negative slope toe a positive slope around it. So we&#x27;ll say there is a local minimum at the point of zero to there is a local maximum at the 0.24 because it does change directions there as well and a changing from a positive slope to a negative slope. Now, for the absolute extreme, there is no absolutely smallest value because this curve is just going to keep going down without bounce. So it&#x27;s a going to negative infinity. So I will put no absolute minimum, the absolute maximum. While this largest function value we get is for yes, we will say there is an absolute maximum at the point of four. I&#x27;m sorry to four

Problem

For graph of a function $y=f(x),$ find the absolu…

Problem 50 Easy Difficulty

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)

Answer

(4,4) , (5,0)

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(4,4) , (5,0)

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Michael SullivanAlgebra and Trigonometry

Grace H.

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Michael Sullivan

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