Sketching the Derivative Function

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. This is a part of the VCE Maths Methods course under the topic Calculus and sub-part Applications of Differentiation.

This post will help you to:

Deduce from the sign of the first derivative whether a function is increasing, decreasing or stationary at a given point or in a given interval
Use the first derivative to find intervals over which a function is increasing or decreasing, and where its stationary points are located
Use the first derivative to investigate a stationary point of a function over a given domain, classifying it as a local maximum, local minimum or neither

This information forms a framework for sketching the derivative function.

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.