stationary point

find the stationary point of the function
z=4x^2+10xy+4y^2-x^2y^2
and also determine their nature
plz show me step i don't know it

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asked by samara
  1. You need both partials to be zero. That is,

    #1: 3y^3 + 2xy = 0
    #2: 3(3x+1)y^2 + x^2 = 0

    From #1, we get x = -3y^2/2
    Plug that into #2 and you get y^2 = 4/15

    So, z has stationary points at (-2/5, ±2/√15)

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    posted by Steve

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