Calculus › Section N · Functions of several variables › Topic N.8
Extrema of functions of two variables
One-variable calculus hunts peaks and valleys with a sign chart. Surfaces have peaks, valleys and a third kind of point, the saddle, and a single discriminant sorts all three.
In this topic
- Peaks, valleys and saddles
- Relative extrema, defined
- Critical points: where extrema can hide
- Worked example: hunting critical points
- The second partials test
- Worked example: classifying the four points
- Saddle points
- Absolute extrema on a closed region
- Worked example: scanning a square
- Common mistakes to avoid
- Key takeaways
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Standards: Beyond AP