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Thread: Lagrange Multiplers: Why is this answer DNE

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    Lagrange Multiplers: Why is this answer DNE

    Lagrange Multiplers: Why is this answer DNE-capture.png

    I am getting values for x and y
    x= sqrt(7/8) and y= 7/(sqrt(7/8))

    the equations i get:

    2xy+1=ylambda
    x^2+1=xlambda

    the equation i get from setting lambdas equal to eacher : (2xy+1)/y = (x^2+1)/x

    solve for y in terms of x, y = x/(x^2+1-2x^2)

    plugging y (x) into my constraint of xy=7 , i solve for x=+/- sqrt(7/8). and i also get a value for y. Plugging these x,y for f(x,y), i get a value... why is the answer in the answer key DNE??
    Last edited by lc99; Oct 28th 2018 at 02:16 PM.
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    Re: Lagrange Multiplers: Why is this answer DNE

    Apply the second partials test to see that both of the critical points are saddles.
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    Re: Lagrange Multiplers: Why is this answer DNE

    how come the lagrange multipliers doesnt work? How do i make sure it gives valid answer? When i apply the theorem, I having getting a critical point which works and returns a value...

    Whenever I do lagrange multipliers, do i always have to check using the second partials test?
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    Re: Lagrange Multiplers: Why is this answer DNE

    Quote Originally Posted by lc99 View Post
    how come the lagrange multipliers doesnt work? How do i make sure it gives valid answer? When i apply the theorem, I having getting a critical point which works and returns a value...

    Whenever I do lagrange multipliers, do i always have to check using the second partials test?
    The Lagrange multiplier method finds extrema.

    You have to apply the second partials test to determine what kind of extrema they are.

    They could be maxima, minima, or saddle points which are neither.
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