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    Please help! Working through old exam papers as revision and really stuck on this question:

    Find and classify all stationary points of the following function:

    f(x,y)= x^2 + 12xy + 3xy^2 + y^3

    I know you have to set the first derivatives to zero and then evaluate D=d^2f/dx^2 . d^2f/dy^2 - (d^2f/dxdy)^2 but I'm not sure how to find the points from the first derivatives? Is this just a huge brain fart and is actually really easy? Lol, any help appreciated
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    (Original post by Vianna)
    ...
    One way:

    From df/dx=0 you can re-arrange to get 2x=....

    Then sub into df/dy=0, eliminating the x, and simplify.

    Where the d's are partial derivatives, of course - just can't be arsed to LaTex it.

    It looks horrendous, but it's straight forward to solve for y.
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    (Original post by Vianna)
    Please help! Working through old exam papers as revision and really stuck on this question:

    Find and classify all stationary points of the following function:

    f(x,y)= x^2 + 12xy + 3xy^2 + y^3

    I know you have to set the first derivatives to zero and then evaluate D=d^2f/dx^2 . d^2f/dy^2 - (d^2f/dxdy)^2 but I'm not sure how to find the points from the first derivatives? Is this just a huge brain fart and is actually really easy? Lol, any help appreciated
    Set the first derivatives to zero
    Solve the equation system for (x,y) simultaneously
    Subtract df/dx=0 from df/dy=0, arrange to y then substitute this in the df/dx=0 and factorize
    You will get 3 solutions
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    (Original post by ghostwalker)
    One way:

    From df/dx=0 you can re-arrange to get 2x=....

    Then sub into df/dy=0, eliminating the x, and simplify.

    Where the d's are partial derivatives, of course - just can't be arsed to LaTex it.

    It looks horrendous, but it's straight forward to solve for y.
    Thanks! All sorted now
 
 
 
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