Find: f ( x , y ) = y 2 + x 2 y + x 2 − 2 y

Question

Find:  f  (  x  ,  y  )  =      y    2    +      x    2    y  +      x    2    −  2  y

Frances Dodson · Accepted Answer

f          x                =        2        x        +        2        x        y        =        0                                      f          y                =                  x          2                +        2        y        −        2        =        0            From this point you got   2  x  y  =  −  2  x and then   y  =  −  2  x      /    2  x  =  −  1 but we cannot do the last step, because   x can be zero. The correct procedure is to take common factor:   2  x  (  1  +  y  )  =  0 and see we have two possibilities,   x  =  0 and   1  +  y  =  0. The first one, plugged in the second equation completes the missing solution.

Find:f(x,y)=y^2+x^2y+x^2−2y

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