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 , then it will occur at one of the critical numbers of the function defined by . In this section, we need to set up the system of equations:
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