This document discusses points of inflexion, which are special points (SPs) on a curve where the gradient is the same before and after. It uses the example function y=x^3 to show that at x=0, the gradient dy/dx is 0, making this a point of inflexion. A table is included to illustrate that the gradient is the same on both sides of x=0, confirming it is a point of inflexion. The key things to learn are what a point of inflexion is, how to identify them by looking for places where the gradient is the same on both sides, and that they occur at SPs where the second derivative is 0.

1. Block 1
Points of Inflexion
The other Type of SP

2. What is to be learned?
• What a P of I is
• How to tell if you have a P of I

3. Ex y = x3
For SPs dy
/dx = 0
dy
/dx = 3x2
3x2
= 0
x = 0
y = 03
SP is (0 , 0)
Nature?

4. Nature Table
y = x3 dy
/dx = 3x2
x 0
dy
/dx = 3x2
slope
-1 1
0+ +
Point of Inflexion at (0 , 0)

5. What does it look like?
Point of Inflexion

6. Point of Inflexion
SP where gradient is before and
after.
the same
or
Point of Inflexion

7. Point of Inflexion
SP where gradient is before and
after.
the same
or
Point of Inflexion