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spndsh

  • 3 years ago

lagrange multipliers: f(x,y,z)= x-2y+5z; g(x,y,z)= x^2+y^2+z^2=30

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  1. Algebraic!
    • 3 years ago
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    you found both gradients I assume?

  2. spndsh
    • 3 years ago
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    |dw:1352428589155:dw|

  3. Algebraic!
    • 3 years ago
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    \[(\frac{ 1 }{ 2\lambda } )^2 + (\frac{ -1 }{ \lambda } )^2 + (\frac{5 }{ 2\lambda } )^2 =30\] \[(\frac{ 1 }{ 2} )^2 + (-1 )^2 + (\frac{5 }{ 2 } )^2 =30\lambda^2\]

  4. Algebraic!
    • 3 years ago
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    \[\lambda = 1/2\]

  5. spndsh
    • 3 years ago
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    x= 1 ; y=2 ; z=5 .. how do find the max/mins?

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