The monotony scheme
From the signs of the derivative on every gap, mark with arrows where the function rises ↗ and falls ↘, and find the extreme points.
- Germany: grade 11
- Ukraine: grade 10
- Russia: grade 11
Guide
This follows the Ukrainian Grade 10 course (algebra and calculus, section 3, items 22-25). The zeros of the derivative cut the number line into gaps; on each gap f′ keeps one sign. If f′(x) > 0 the function increases (↗); if f′(x) < 0 it decreases (↘). A change from + to − is a maximum point, from − to + a minimum point.