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Lagrange Multipliers - basic which value?

  • Thread starter rocomath
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(1) [tex]f(x,y,z)=x+2y[/tex]
(2) [tex]x+y+z=1[/tex]
(3) [tex]y^2+z^2=4[/tex]

[tex]1=\lambda[/tex]
[tex]2=\lambda+2y\mu[/tex]
[tex]0=\lambda+2z\mu[/tex]

[tex]u=\frac{1}{2y}[/tex]
[tex]y=\pm\sqrt2 \ \ \ z=\pm\sqrt2[/tex]

Plugging into equation 2 to solve for x.

How do I know to use either [tex]y=\sqrt 2 \ \mbox{or} \ y=-\sqrt2[/tex] ... similarly with my values for z.

edit: NVM, I'm an idiot :p I overlooked a step, which told me that [tex]z=-y[/tex]

... too late to delete?
 
Last edited:

Answers and Replies

351
2
see the geometry (It's a plane)

f(x,y) = ..

I was thinking about f_xx*f_yy - (f_xy)^2 thing,
but my teacher says it's very hard to *identify* max min in Lagrange; should use geometry
 
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