Difference between revisions of "Math 22 Lagrange Multipliers"
Jump to navigation
Jump to search
| Line 1: | Line 1: | ||
==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 (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle g(x,y)=0}
, then it will occur at one of the critical numbers of the function defined by
Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\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}
This page were made by Tri Phan