optimizacion 2018-11-29 17_31_42.pdf

optimizacion 2018-11-29 17_31_42.pdf - Maximun and Minimun...

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Maximun and Minimun Values Adriana Acosta 1 Facultad de ingenieria Universidad de la Sabana Adriana Acosta Maximun and Minimun Values
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Maximun and Minimun Values Definition:Maximun and Minimun Values maximum : A function of two variables has a local maximum at ( a, b ) if f ( x, y ) f ( a, b ) when ( x, y ) is near ( a, b ). The number f ( a, b ) is called a local maximum value. minimum : If f ( x, y ) f ( a, b ) when ( x, y ) is near ( a, b ), then f has a local minimum at ( a, b ) and f ( a, b ) is a local minimum value. Adriana Acosta Maximun and Minimun Values
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Theorem: Maximum or minimum If f has a local maximum or minimum at ( a, b ) and the first-order partial derivatives of f exist there, then f x ( a, b ) = 0 and f y ( a, b ) = 0. Definition: Critital Point A point ( a, b ) is called a critical point (or stationary point) of f if f x ( a, b ) = 0 and f y ( a, b ) = 0, or if one of these partial derivatives does not exist. Adriana Acosta Maximun and Minimun Values
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Second Derivatives Test Suppose the second partial derivatives of f are continuous on a disk with center ( a, b ), and suppose that f x ( a, b ) = 0 and f y ( a, b ) = 0 [that is, ( a, b ) is a critical point of f ]. Let D = D ( a, b ) = f xx ( a, b ) f yy ( a, b ) - [ f xy ( a, b )] 2 If D > 0 and f xx ( a, b ) >
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  • Spring '18
  • Josefina
  • Critical Point, y1, Minimun Values, Adriana Acosta

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