WEBVTT
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So the domain for this one is exes, All
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riel and the intercepts are zero. Just have 10
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pi over four. There is an even symmetry to
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this craft and the Assam totes. What's so for
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those? So the limit as X approaches infinity over
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function Inverse tangent E to the X. Let's pie
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or two. So with X approaches infinity, We
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have an s in tow at Why equals pi over
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too. And now, for the 2nd 1 limit
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as X approaches negative infinity of in verse 10 of
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e to the X. That's going to give us
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zero. So we have as X approaches Negative infinity
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, Why is going to be zero? Okay.
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And now let's look for increasing decreasing intervals. So
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why prime equals e to the X over Okay to
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the two X plus one. And if we dreaded
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to find the critical points, will see that this
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is inconclusive. This is inconclusive. Um, but
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we can look forward the con cavity. So the
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second derivative Well, give us negative e to the
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x times e to the two x minus one over
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e to the two x plus one squared crucial room
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equal zero so we can see X equals zero.
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That's a point we're gonna be looking at North.
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Second derivative test. This is F double prime,
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looking for Khon cavity. You see that? It's
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Khan gave up to the left of zero and Khan
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came down to the right of zero. All right
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, so using this information, we can graph,
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So we have zero pi over four. So I'm
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gonna say this is pi over four. So that
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is, um, our intercept. And we have
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Oh, we have an s in tow. A
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cz x approaches infinity. So we have y equals
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pi over too. All right, So if this
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is pi over four than pie over to must be
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here, all right? And then we have y
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equals zero, as are other Ask him to.
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And now our graph. Oh, so we see
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that this is an inflection point that's important, cause
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we have a switching con cavity. So here we
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have, um, as X approaches infinity, it's
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gonna go to, but it's gonna approach but not
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touch or ask them to at pi over too.
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So this is infinity. The exes are approaching infinity
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, so it's gonna go this way, and negative
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infinity will approach. Why equals zero