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Problem 43 Medium Difficulty

Use the guidelines of this section to sketch the curve.

$ y = 1/(1 + e^{-x}) $

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Video Transcript

So ultimately, our goal for this problem is to sketch the curve. Um, and in sketching the curve, what we'll see is a lot of really important, um, piece of information particularly relating to derivatives and second derivatives. So what this graph is is one over one plus either the negative X So this is the graph right here, and we'll zoom in to see it. Um, we see that this graph is always increasing. Um, it has horizontal Assam totes of zero and one. We see that there's only a white intercept at zero is your 0.5. There are no X intercepts. These are all important piece of information. We can also look at the first derivative and see that there are no critical points. There are no local minimums or maximums. Aan den. We could look at the second derivative and see that there is an inflection point. The graphics con cave up mostly, um, from negative Earth's entirely con cave up from negative infinity to zero and then a 00 is the inflection point. We c 01 half is the inflection point. So from zero on to infinity the graphics conclave down This just shows you how the derivative can be really powerful tool. Um, to help us understand better what this graph actually looks like.