How do I sketch the derivative function?
In this post, we will learn how to sketch the derivative function (or gradient function) for a given graph of a function, without the use of algebraic techniques and in a variety of contexts including motion in a straight line, as a part of the Prelim Maths Advanced course under the topic Calculus and sub-part The Derivative Function and its Graph.
We will establish that f'(x)=0 at a stationary point, f'(x) > 0 when the function is increasing and f'(x) < 0 when it is decreasing, to form a framework for sketching the derivative function. We will also identify families of curves with the same derivative function and use technology to plot functions and their gradient functions.
This video will outline the process that is undertaken when sketching the derivatives of a function, going into an in-depth explanation of the properties of the derivative function relative to its original graph.