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(a) It, for f: AC R + R, at Xo, Ak > 0 for k odd, or Ag < 0 for k even, then show that f cannot have a (local) minimum at xo. b) If A < O for k even, prove that f has a saddle point at xo.

(a) It, for f: AC R + R, at Xo, Ak > 0 for k odd, or Ag < 0 for k even, then show that f cannot have a (local) minimum at xo. b) If A < O for k even, prove that f has a saddle point at xo.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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(a) If, for f: A c R" - R, at xo, A, > 0 for k odd, or Ag < 0 for k even, then show that f cannot have a (local) minimum at xo. (b) If Ag < 0 for k even, prove that f has a saddle point at xo.
Transcribed Image Text:(a) If, for f: A c R" - R, at xo, A, > 0 for k odd, or Ag < 0 for k even, then show that f cannot have a (local) minimum at xo. (b) If Ag < 0 for k even, prove that f has a saddle point at xo.
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