If the X data are not equally spaced, this method may not produce a reliable result. Missing values are ignored.įor evenly-spaced X data, you can apply Savitzky-Golay smoothing. The derivative at a given point is computed by taking the average of the slopes between the point and its two closest neighbors. And we don't see that over here, so we could feel good that its derivativeĪctually isn't depicted.This function performs simple derivative calculations on a data set. This magenta curve looks like an upward opening U. It's getting more and more and more and more positive. It's getting less and less and less and less negative, all the way until the derivative More and more negative until about that point. Tangent line is getting more and more and more and more negative, right until about that point.
Look something like this over the interval. So over here, the derivative of this, so right now we have a positive slope of our tangent line is getting And if you wanted, just for safe measure, you could try to sketch out what the derivative of And then if this is f prime, the derivative of that is That this is actually f, and then this would be f prime. So this brown graph does indeed look like the derivative of this blue graph. Roughly just sketched out looks an awful lot like theīrown graph right over here. And then it just looks like it is, the slope is getting moreĪnd more and more negative, so our derivative is gonna get more and more and more negative. Right over here, ourĭerivative would be zero. So it might look something like this where over here it'sīecoming less positive again, less positive, less But then right around here it seems like it's getting less positive again. So we see here our derivative becomes more and more positive. And at this point it crosses the x-axis and it becomes more and more positive. It would start out negative, and it would become lessĪnd less and less negative. Less and less negative until we go right over here What would its derivative look like? So over here our slope is quite negative, and it becomes less and So maybe we could say that this is f and that this is f prime. So I would actually say that this is a good candidate for being, the third function is a good candidate for being the derivative It fell off of the part of the graph that we actually showed. Might look something like this, we just didn't see it. Slope would become zero, which would be right around there. Will become less and less and less negative, and then at this point our To roughly right over there, then over here our slope Graph is indeed the derivative of this first graph, then what we see is ourĭerivative is negative right over here, but then right around here it But in this case, it could just be 'cause we don't see theĮntire original function. Has more extreme points, more minima and maxima Now, one thing that mightīe causing some unease to immediately say that this last graph is the derivative of the first one is we're not used to situations where the derivative And this graph is negative when the slope of the tangent This graph is positive when the slope of the tangent And at least over this interval, it seems it's positive from here to here. X-axis at the right place right over there. But what about this magenta graph? It does look like it has the right trend. So we can rule out the blue graph as being the derivative Negative to positive, as opposed to going from Over that interval, it's going from being Now, we could immediately tell that this blue graph is not the derivative of this orange graph. More and more negative, at least over the interval that we see. Is gonna cross zero, 'cause our derivative is zero there, slope of the tangent line. So the derivative of thisĬurve right over here, or the function represented by this curve is gonna start off reasonably Slope is going to be zero, and then it becomes more and more and more and more negative. Is quite positive here, but then it becomes lessĪnd less and less positive, up until this point where the Here in this orange color, we can see that the slope Of each of these graphs, or the functions It is I'm gonna try to sketch what we can about the derivatives Is the first derivative, and which is the second? Like always, pause this video and see if you can work through it on your own before we do it together. Of them is the function f, another is the first derivative of f, and then the third is the Graphs of three functions here, and what we know is that one
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