HSC Together Year 12 Maths Advanced: First Derivative of the Graph of a Function

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# First Derivative of the Graph of a Function

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

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