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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