HSC Together Year 11 Maths Advanced: Sketching the Derivative Function

• Working With Functions
• Trigonometric Functions
• Calculus
• Exponential and Logarithmic Functions
• Statistical Analysis
• Back to other subjects
Back to other subjects

# 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, 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.

### 45,861 students have a head start...

Get exclusive HSC content & advice from our team of experts delivered weekly to your inbox!

## Here’s how we help...

### Holistic K-12 Tutoring

Attend our master-class workshops on how to ace your essays, assessments and exams!

### Comprehensive Workshops

Attend our master-class workshops on how to ace your essays, assessments and exams!

### Study, Uni, Career Mentoring

Attend our master-class workshops on how to ace your essays, assessments and exams!

### Senior School Workshops

Attend our master-class workshops on how to ace your essays, assessments and exams!

## 45,861 students have a head start...

Get exclusive study content & advice from our team of experts delivered weekly to your inbox!