Difference between revisions of "Math 22 Lagrange Multipliers"
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==Method of Lagrange Multipliers== | ==Method of Lagrange Multipliers== | ||
If <math>f(x,y)</math> has a maximum or minimum subject to the constraint <math>g(x,y)=0</math>, then it will occur at one of the critical numbers of the function defined by | If <math>f(x,y)</math> has a maximum or minimum subject to the constraint <math>g(x,y)=0</math>, then it will occur at one of the critical numbers of the function defined by | ||
| − | <math>F(x,y,\lambda)=f(x,y)-\lambda g(x,y)</math> | + | <math>F(x,y,\lambda)=f(x,y)-\lambda g(x,y)</math>. |
| + | |||
| + | In this section, we need to set up the system of equations: | ||
| + | |||
| + | <math>F_x(x,y,\lambda)=0</math> | ||
| + | <math>F_y(x,y,\lambda)=0</math> | ||
| + | <math>F_{\lambda}(x,y,\lambda)=0</math> | ||
| + | |||
| + | |||
Revision as of 08:45, 18 August 2020
Method of Lagrange Multipliers
If has a maximum or minimum subject to the constraint Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle g(x,y)=0}
, then it will occur at one of the critical numbers of the function defined by
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle F(x,y,\lambda)=f(x,y)-\lambda g(x,y)}
.
In this section, we need to set up the system of equations:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle F_x(x,y,\lambda)=0}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle F_y(x,y,\lambda)=0}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle F_{\lambda}(x,y,\lambda)=0}
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