This is part of the HSC Mathematics Advanced course under the topic of Calculus: Differential Calculus.
In this post, we will explore the first derivative of the graph of a function. This includes learning about how to use the first derivative to investigate the shape of the graph of a function. This will be in conjunction with learning 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
- Determine the greatest or least value of a function over a given domain (if the domain is not given, the natural domain of the function is assumed) and distinguish between local and global minima and maxima
Eddie Woo: Sketching a Derivative from the Graph of a Function
Introduction to Max/Min Problems
Relative Extrema, Local Maximum and Minimum, First Derivative Test, Critical Points
Application of Calculus Examples
Calculus Sketching Example 1
Calculus Sketching Example 2
Calculus Sketching Example 3
