Chapter 13 Handout

Chapter 13 Handout - 2. f xx > 0 f yy...

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Chapter 13 Handout: Multivariate Optimization Let z = f(x, y) and let ( x c , y c ) be a critical point of f(x, y) For ( x c , y c ) to be a Local Maximum , then Local Minimum , then Saddle Point , then Inflection point , then 1. f x = 0 f y = 0 Must hold as a system, i.e., you have to solve it as a system. [this identifies ( x c , y c )] 1. f x = 0 f y = 0 Must hold as a system, i.e., you have to solve it as a system. [this identifies ( x c , y c )] 1. f x = 0 f y = 0 Must hold as a system, i.e., you have to solve it as a system. [this identifies ( x c , y c )] 1. f x = 0 f y = 0 Must hold as a system, i.e., you have to solve it as a system. [this identifies ( x c , y c )] 2. f xx < 0 f yy < 0 Must hold simultaneously. You may have to substitute ( x c , y c ) into f xx and f yy to obtain their values.
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Unformatted text preview: 2. f xx &amp;gt; 0 f yy &amp;gt; 0 Must hold simultaneously. You may have to substitute ( x c , y c ) into f xx and f yy to obtain their values. 2. f xx &amp;lt; 0 f yy &amp;gt; 0 OR f xx &amp;gt; 0 f yy &amp;lt; 0 Must hold simultaneously. You may have to substitute ( x c , y c ) into f xx and f yy to obtain their values. 2. f xx &amp;gt; 0 f yy &amp;gt; 0 OR f xx &amp;lt; 0 f yy &amp;lt; 0 Must hold simultaneously. You may have to substitute ( x c , y c ) into f xx and f yy to obtain their values. 3. f xx *f yy &amp;gt; (f xy ) 2 3 . f xx *f yy &amp;gt; (f xy ) 2 3. f xx *f yy &amp;lt; (f xy ) 2 3. f xx *f yy &amp;lt; (f xy ) 2 STEP 1 identifies any critical point(s). STEP 2 and STEP 3 tell you the nature of the critical point(s)....
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