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Say I have a curve on an x-y graph. And say it is too "anomalous" to categorize as one of the well known graphs (example is y=x, y=1/x etc). How would I be able to graph the first derivative of this unstable curve?

Should I be using the following equation to find out?

$f'(a)=\lim _{h\to 0}{\frac {f(a+h)-f(a)}{h}}$

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1 Answer

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Usually the goal is to recognize some of the common features of a graph, such as the minimas and maximas as well as the inflection points.

So, think about the minimas and maximas. You have a minima and a maxima when the derivative is zero, right? So, find your minimas and maximas and plot a zero for the derivative at that x-location.

Now, look at the direction that the curves are pointing. If the curves are sloped up, the derivative will be positive. If the curves are sloped down, the derivative will be negative.

Now, look at the inflection points on your graph. Those are where the 2nd derivative is zero, so these will be the minimas and maximas of your first derivative.

Using that information, you can usually make a basic sketch of a derivative of an unknown function.

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