WEBVTT
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okay. To find the vertical and horizontal ascent of
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effort back, we have to personal. We have
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to examine the domain of the function. So the
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national companies are all X rated Indio. So the
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inside on minus Alan X's graves and Jiro you get
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one is greater than Eleanor Vex, and you take
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E on both sides and that is greater than Excell
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Access Western E sort of domain is essentially from zero
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tio. That is the domain of our function.
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So what does that tell us? Well, we
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know that this is a natural like furniture we notice
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continuous between zero you. But it doesn't mean that
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there could be a vertical acids are occurring at the
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imports. So we can evaluate that by plugging in
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that limit the limit of exit go studio FX.
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So if you plug in zero, you get national
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level one and international art of zero is negative Infinity
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. So you get negative to the positive. So
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naturally, one thousand phonies Incredibly, Which is it
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going to Trinity? So there is a ah vertical
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hospital recurring and X equals zero, and it goes
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off the positive meaning if you got a e from
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the left of effort. Beck, you get natural
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log one minus. And at National Aga is just
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for one. So one minus one is zero national
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log of zero gives us negative infinity. So that's
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also going off to if every so we have a
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X equals zero and e for a horizontal. Lassiter
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, Um, there is done because we have such
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a strict or maine. So she take eliminate excess
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in Trinity, who we've technically already evaluated tea and
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point. So no words are to find where the
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functions increasing, decreasing. We have to find first
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derivative test. No problem. This will come out
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to negative one over X times one minus our Next
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we looked for the critical numbers of dysfunction. So
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that's where the bottom could possibly equals zero and so
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e we know that it could happen at zero,
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which is already part of our domain. Still,
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we'LL evaluate it, Teo. And in one minus
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l. A durex that occurs when Deccan equals zero
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when it is e so is it was the act
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which again is the end of our domain. So
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we're going to die away from zero to a and
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we don't care about anything outside of that. Ah
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, you fucking value between Juni get negative numbers.
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So we know it is decreasing the entire time on
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its interval, decreasing for all the t e.
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There is no local maxim and because there's no change
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and the direction of the function, so to find
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the con cavity of the function would take the second
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derivative and that comes out to be negative. Allan
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of X all over X times one minus Alan Rex
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, this equals zero and exes Ical too one.
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And we again on critical number. That kind of
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your own e. So we're going to evaluate it
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at tio ese are signed chart. It's going to
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happen around zero one and e and we ignore everything
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outside of it. So between your number zero on
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one, you get positive numbers and repugnant Other shouldn't
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want need and negative numbers. It is currently rub
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down. You can take off from zero to one
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, and Kong came down from Plan Tio. According
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to D, Now we have we have to have
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an inflection point occurring at X equals one is a
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tactical one. In fact point Ah, now we
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have enough information to draw a graph of the function
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, and we know that it is the limited between
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June and Jesus will be like somewhere over here wherever
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I set that to be and it is decreasing the
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entire time. So it's coming. Remember when As
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limited excess dealer who's going to positive for? So
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we know it starts up here. It was going
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to come down, come down, come down,
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have a conclave up ship until one. So it's
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going to kind of have a U shape, but
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at one and switches and it actually goes to a
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con cave down shape and it goes off to negative
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infinity. It goes like that. This is this
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is e here and just basically the crab. And
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this is, uh, zero. This is that
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one, and this is a graph of Catholics.