So, our slope is positive and decreasing, and then right over about Then it becomes negative, but decreasing, all the way until this point, which is at x equals negative one. Is decreasing right over here, our slope will be decreasing. On the derivative, theĭerivative is decreasing, which means the slope of our tangent line of our original function isĭecreasing, and we saw that. So, here we can see the interesting parts. This is the derivative of our original blue function. Point is when our slope goes from increasing to decreasing or from decreasing to increasing. But you could also tell inflection points by looking at your first derivative. So, that's how you could tell it just from the function itself. It's negative, it stillĭecreases, x equals negative one, and then our slopeīegins increasing again. So, let me show you that again now that the point is labeled. But that at this point right over here, we have an inflection point, So, something interesting happened right at x equals negative one, and so that's a pretty good indication. Get, it looks like we get to about x equals negative one, and then our slopeīegins to increase again. Then it goes negative, and the slope keeps decreasing, all the way until we And then as we increase x, we can see that the slope is So, when x is equal to negative two, that is what the tangent line looks like. The graph of some function, and let me draw the slope of a tangent line at different points. Is a point on our graph where our slope goes fromĭecreasing to increasing or from increasing to decreasing. So, the first thing to appreciate is an inflection point To do in this video is try to get a graphical appreciationįor inflection points, which we also cover in someĭetail in other videos.
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