# Differentiation Revision Notes for Core 2

Some notes that I created for differentiation for Core 2.

- Created by: George
- Created on: 12-05-11 21:53

First 207 words of the document:

Mathematics Core 2 Differentiation

Increasing and Decreasing functions

Increasing functions are functions that have a gradient greater than 0.

So dy / dx > 0.

You can work if a function is an increasing function if you differentiate the term and then see if

at the point you are considering the gradient is greater than 0.

For example:

If we need to show that the function of x 2 is an increasing function at 2.

dy / dx = 2x

2 x 2 = 4 of which is greater than 0, so it is an increasing function.

Decreasing function are functions that have a gradient less than 0.

So dy / dx < 0.

You can work if a function is a decreasing function if you differentiate the term and then see if

at the point you are considering has a gradient is less than 0.

For example:

If we need to show that the function of x 2 is an increasing function at 2.

dy / dx = 2x

2 x 2 = 4 of which is less than 0, so it is a decreasing function.

Summary

dy / dx > 0 is an increasing function

dy / dx < 0 is a decreasing function

dy / dx = 0 is a stationary point or turning point

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