Posted by Lucy on Monday, February 27, 2012 at 12:54am.
Find and classify all local minima, local maxima, and saddle points of the function f(x,y)= 3yx^23xy^2+36xy

cal3  Steve, Monday, February 27, 2012 at 12:38pm
F = 3yx^23xy^2+36xy
Fx = 6xy  3y^2 + 36y
Fxx = 6y
Fy = 3x^2  6xy + 36x
Fyy = 6x
Fxy = 6x  6y + 36
D = FxxFyy(Fxy)^2 = 36xy  36(x+y6)^2
Fx = 0 Fy=0 at (0,0)
D<0 so a saddle point
Fx = 6xy  3y^2 + 36y
Fx = 0 when y = 2(6x)
Fy = 3x^2  6xy + 36x
Fy = 0 when x = 2(6y)
So there is a local max for z along those two lines

cal3  Lucy, Monday, February 27, 2012 at 6:12pm
Okay Im just confused as how to get Fx=0 and Fy=0, If I set 6xy3y^2+36y=0 how do i solve this?? Algebra was so long ago!
could you detail that part of the problem...
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