Functions – Increasing, Decreasing & Stationary

PointsClaire Powis

Increasing Functions

Decreasing Functions

Changing Functions

Example 1

Example 2

Questions

Stationary Points: f’(x) = 0

Maximum and minimum points are sometimes called ‘turning points’ as the graph changes direction at these points.

Some graphs can have more than one stationary point:

Stationary Points: f’(x) = 0

What is a point of inflexion?

Example 3

A curve has equation . Determine, by calculation, the coordinates and nature of the stationary points if the curve.

Steps:1. Differentiate the function to find y’2. Set y’=0 to find stationary points3. Find points either side of stationary points to

work out whether maximum, minimum or point of inflexion.

Example 4

=

= for = 1, =

( 1; -11) ( ; )Maximum Minimum

Solution

Solving Problems