SL 5.2—Increasing and decreasing functions
- Syllabus
- First assessment 2021
- Objective
- —
- Level
- HL
The first derivative reveals where a function rises or falls
The first derivative reveals where a function rises or falls.
If f′(x)>0 the graph increases and if f′(x)<0 it decreases; sign changes identify possible stationary extrema.
Example
For f′(x)=x−2, the function decreases before x=2 and increases after it, so x=2 is a local minimum.
Make a sign chart around every critical value rather than relying on the derivative being zero alone.
A stationary point can be a saddle or inflection; f′=0 is a candidate, not a classification.