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Find the critical points of the function f(x,y)=x^3-6xy+3y^2-24x+4 Also classify them in Relative Maxima, Relative Minima and Saddle Points.

  • 10 months ago
  • 10 months ago

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  1. AlHajri
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    First find the first partial derivatives (fx) and the first partial derivative (fy). fx= 3x^2-6y-24=0 fy=-6x+6y=0 From these two equations you find the two critical points which are (-2,-2) and (4,4) After that you use the second derivative test (D=fxxfyy-(fxy)^2) In the case of (-2,-2) D<0 and so it is a saddle point. In the case (4,4) D>0 and fxx<0 and so it is a minimum point

    • 10 months ago
  2. alirazamarchal
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    Thank you very much...

    • 10 months ago
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