MATH 200 Lecture Notes - Lecture 7: Maxima And Minima, Saddle Point, Multiple Integral

• School: Drexel University
• Department: Mathematics
• Course: MATH 200
• Professor: unknown

Document Summary

13. 8: maxima and minima of functions of 2 variables (xo,yo) A function of 2 variables is said to have a relative minima at. A function of 2 variables is said to have a relative maximum at (cid:4666)(cid:1876)(cid:3042),(cid:1877)(cid:3042)(cid:4667) if there is a disk centered at (cid:4666)(cid:1876)(cid:3042),(cid:1877)(cid:3042)(cid:4667) so that (cid:1858)(cid:4666)(cid:1876)(cid:3042),(cid:1877)(cid:3042)(cid:4667)(cid:3410) (cid:1858)(cid:4666)(cid:1876),(cid:1877)(cid:4667) for all (x,y) in that disk. F is said to have an absolute maximum at (cid:4666)(cid:1876)(cid:3042),(cid:1877)(cid:3042)(cid:4667)if (cid:1858)(cid:4666)(cid:1876)(cid:3042),(cid:1877)(cid:3042)(cid:4667)(cid:3410)(cid:1858)(cid:4666)(cid:1876),(cid:1877)(cid:4667)for all (x,y) in the (cid:4666)(cid:1876)(cid:3042),(cid:1877)(cid:3042)(cid:4667) if there is a disk centered at (cid:4666)(cid:1876)(cid:3042),(cid:1877)(cid:3042)(cid:4667) so that (cid:1858)(cid:4666)(cid:1876)(cid:3042),(cid:1877)(cid:3042)(cid:4667)(cid:3409) (cid:1858)(cid:4666)(cid:1876),(cid:1877)(cid:4667) for all (x,y) in that disk. F is said to have an absolute minimum at (cid:4666)(cid:1876)(cid:3042),(cid:1877)(cid:3042)(cid:4667)if (cid:1858)(cid:4666)(cid:1876)(cid:3042),(cid:1877)(cid:3042)(cid:4667)(cid:3409)(cid:1858)(cid:4666)(cid:1876),(cid:1877)(cid:4667)for all (x,y) in the. If f has a relative max or relative min at (cid:4666)(cid:1876)(cid:3042),(cid:1877)(cid:3042)(cid:4667) then we say f has a relative extremum at (cid:4666)(cid:1876)(cid:3042),(cid:1877)(cid:3042)(cid:4667) If f has an absolute max or an absolute min at (cid:4666)(cid:1876)(cid:3042),(cid:1877)(cid:3042)(cid:4667)then we say f has an absolute extremum at (cid:4666)(cid:1876)(cid:3042),(cid:1877)(cid:3042)(cid:4667) domain.