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.
The following videos will explore curve sketching in more detail.
Want to learn more? Check out more of our VCE Mathematics resources here!