1. Maximum and Minimum Points

2. Types of turning points
There are two types of turning points
Minimum
Maximum
For each of these turning points:
ie. the gradient is 0
Types of turning points

3. Example Find the coordinates of the turning point on the graph of
. Determine its nature.
Answer:
for a turning point
To find the y coordinate: sub x into y= equation
To find whether max or min (ie. determining its nature) look at the gradient (y’) either side of x=3
Positive to right
Example
Negative to left

4. Determine the coordinates of the turning points of the function
. State which point is a maximum and which is a minimum.
Example 2