Here's my work on this problem.
(df/dx)=6xy-6x = y-1....(1)
(df/dy)=3(x^2)-6y+(3y^2) = (x^2)-2y+(y^2)......(2)
since (df/dx)=0=(df/dy)
hence from (1) we get y=1, substituting this in (2), i get x=1.
Hence (1,1) is the stationary piont.
have i done this right till here?
Now this is the part where i'm going wrong,
A=(d^2f/dx^2)= 0, B=(d^2f/dxdy)=1 or 2x, C=(d^2f/dy^2)= 2y-2.
I need to find D = B^2 - AC, thus
if D>0, (1,1) is a saddle point,
if D<0, a maximum at (1,1) when A<0 and minimum at (1,1) when A>0.
if D=0, does not give any conclusion.
2007-03-03
14:52:30
·
1 answers
·
asked by
Anonymous
in
Mathematics