Types of Stationary points
There are three types of stationary points:
1. Local Minimum Point: the curve is decreasing on the left and increasing on the right of the maximum.
1. Local Minimum Point: the curve is decreasing on the left and increasing on the right of the maximum.
LHS: f'(x) < 0
Minimum: f'(x) = 0
RHS: f'(x) > 0
2. Local Maximum: the curve is increasing on the right hand side and decreasing on the right hand side of the maximum.
Minimum: f'(x) = 0
RHS: f'(x) > 0
2. Local Maximum: the curve is increasing on the right hand side and decreasing on the right hand side of the maximum.
LHS: f'(x) > 0
Maximum: f'(x) = 0
RHS: f'(x) < 0
3. Points of horizontal inflexion: the curve is increasing or decreasing on both sides of the point of inflexion.
Maximum: f'(x) = 0
RHS: f'(x) < 0
3. Points of horizontal inflexion: the curve is increasing or decreasing on both sides of the point of inflexion.
LHS: f'(x) > 0
Inflexion: f'(x) = 0
RHS: f'(x) > 0
OR
LHS: f'(x) < 0
Inflexion: f'(x) = 0
RHS: f'(x) < 0
For further study watch this video.
See below for some examples:
Inflexion: f'(x) = 0
RHS: f'(x) > 0
OR
LHS: f'(x) < 0
Inflexion: f'(x) = 0
RHS: f'(x) < 0
For further study watch this video.
See below for some examples:
See below for some exercises (the ones on the right are extension):