Math 22 Lagrange Multipliers - Revision history

Tphan046 at 16:57, 18 August 2020

2020-08-18T16:57:09Z

2020-08-18T16:56:41Z

2020-08-18T16:54:34Z

2020-08-18T16:50:05Z

2020-08-18T16:45:45Z

2020-08-18T16:38:40Z

2020-08-18T16:33:59Z

Created page with " '''Return to Topics Page''' '''This page were made by Tri Phan'''"

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[[Math_22| '''Return to Topics Page''']]

'''This page were made by [[Contributors|Tri Phan]]'''

@@ Line 28: / Line 28: @@
 !Solution: &nbsp;
 |-
-|So, <math>F(x,y,\lambda)=f(x,y)-\lambda g(x,y)=xy-\lambda (x+3y-6)=xy-\lambda x -3\lambda y-6\lambda</math>
+|So, <math>F(x,y,\lambda)=f(x,y)-\lambda g(x,y)=xy-\lambda (x+3y-6)=xy-\lambda x -3\lambda y+6\lambda</math>
 |-
 |<math>F_x(x,y,\lambda)=y-\lambda</math>

@@ Line 28: / Line 28: @@
 !Solution: &nbsp;
 |-
-|<math>\frac{\partial z}{\partial x}=2xy^3</math>
+|So, <math>F(x,y,\lambda)=f(x,y)-\lambda g(x,y)=xy-\lambda (x+3y-6)=xy-\lambda x -3\lambda y-6\lambda</math>
 |-
-|<math>\frac{\partial z}{\partial y}=3x^2y^2</math>
+|<math>F_x(x,y,\lambda)=y-\lambda</math>
 |}

@@ Line 15: / Line 15: @@
 !Solution: &nbsp;
 |-
-|<math>\frac{\partial z}{\partial x}=4x^2-4y</math>
+|So, <math>F(x,y,\lambda)=f(x,y)-\lambda g(x,y)=xy-\lambda (x+y-14)=xy-\lambda x -\lambda y+14\lambda</math>
 |-
-|<math>\frac{\partial z}{\partial y}=-4x</math>
+|<math>F_x(x,y,\lambda)=y-\lambda</math>
 |}

@@ Line 8: / Line 8: @@
    <math>F_y(x,y,\lambda)=0</math>
    <math>F_{\lambda}(x,y,\lambda)=0</math>
-−
+'''Example:''' Set up the Lagrange Multipliers:

@@ Line 1: / Line 1: @@
 ==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
-   <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>.

← Older revision	Revision as of 16:38, 18 August 2020
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−	+	==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
	+	<math>F(x,y,\lambda)=f(x,y)-\lambda g(x,y)</math>