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Math Help - Finding critical points

  1. #1
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    Finding critical points

    How do you find the critical points of a function with more than one variable?

    EX:  z=f(x,y)=2x^2+3y^2+xy-3y+3

    I need to find x, y, and z.

    Thank you!
    Last edited by eri123; April 22nd 2010 at 08:57 PM.
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  2. #2
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    Quote Originally Posted by eri123 View Post
    How do you find the critical points of a function with more than one variable?

    EX:  z=f(x,y)=2x^2+3y^2+xy-3y+3

    I need to find x, y, and z.

    Thank you!
    1. Differentiate f(x,y) wrt x and afterwards differentiate f(x,y) wrt y. Both derivations must equal zero.

    2. Solve the system of equations for x and y. Plug in the results into the equation of the function. I've got V\left( -\frac3{23} , \frac{12}{23} , \frac{51}{23}\right) . This is the vertex of the eliptical paraboloid, drawn in red.
    Attached Thumbnails Attached Thumbnails Finding critical points-ellipt_paboloid_vertex.png  
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