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Math Help - critcal points

  1. #1
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    critcal points

    find all the critical points of the function

    f(x,y) = (x-2y)e^(x^2-y^2)

    and classify them as local maxima, local minima or saddle points.


    How is this differentiated?
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  2. #2
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    Quote Originally Posted by manalive04 View Post
    find all the critical points of the function

    f(x,y) = (x-2y)e^(x^2-y^2)

    and classify them as local maxima, local minima or saddle points.


    How is this differentiated?
    You need to find where \left(\frac{\partial f}{\partial x},\frac{\partial f}{\partial x}\right) = 0

    To find \frac{\partial f}{\partial x} differentiate f(x,y) with respect to x holding y constant

    To find \frac{\partial f}{\partial y} differentiate f(x,y) with respect to y holding x constant
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  3. #3
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    Quote Originally Posted by pickslides View Post
    You need to find where \left(\frac{\partial f}{\partial x},\frac{\partial f}{\partial x}\right) = 0

    To find \frac{\partial f}{\partial x} differentiate f(x,y) with respect to x holding y constant

    To find \frac{\partial f}{\partial y} differentiate f(x,y) with respect to y holding x constant

    Can you please explain this further - how is it differentiated i cant work it out
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  4. #4
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    You need to use the product rule it is... f = uv \Rightarrow f'=uv'+vu'

    Differentiating with respect to x (finding \frac{\partial f}{\partial x} ) make

    u = x-2y \Rightarrow u' = 1

    v = e^{x^2-y^2} \Rightarrow v' = 2x\times e^{x^2-y^2}

    Now apply f = uv \Rightarrow f'=uv'+vu'

    After this you need to differentiate for y. (finding \frac{\partial f}{\partial y} )

    Then solve for \left(\frac{\partial f}{\partial x},\frac{\partial f}{\partial x}\right) = 0
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