MATH-M 311 Lecture Notes - Lecture 16: Maxima And Minima

• School: IU
• Department: Mathematics
• Course: MATH-M 311
• Professor: Bhaskar Siddharth

Document Summary

For each critical number, if 2nd derivative positive = minimum; negative = maximum; zero = no info: if , at local min/max , then must be 0. Critical point occurs at and values that satisfy (ie. where and are both 0) If , and or have opposite signs, and point is saddle point. If , no information given; need other method. There can be critical line(s) instead of point(s); for some 2-dimensional figures, like paraboloid. Cylinders, there can be a whole line on which every point is a min, max, or saddle point: representation of gradients at extrema and saddle points: Magnitude of vector is smaller closer to point (less steep increase/decrease closer to extremum) Ex. o o o o o in that order: critical points, classify using second partial derivatives saddle point both 2nd pds positive, so local min both 2nd pds positive, so local min also.