Math Is Fun Forum

Angel Rox

Member

Registered: 2008-11-10

Posts: 15

need help urgently...

Q1 - Find the critical points of the function  f(x,y) = x^2 + 2y^2 - x^2y and then classify them into relative maxima, relative minima and saddle points.

Q2 - Let f(x,y) = xy - x - y + 3 and R is the triangular region with vertices (0, 0), (2, 0) and (0, 4). Find the interior and boundary points only at which the absolute extrema of f(x,y) can occur.

ishaq027

Member

Registered: 2009-04-09

Posts: 1

Re: need help urgently...

Please give me quick Answer
Let f(x,y)=x^2+2y^2-x^2y  and then classify them into relative maxima, relative minima and saddle points

ashfaq

Guest

Re: need help urgently...

Q1 - Find the critical points of the function  f(x,y) = x^2 + 2y^2 - x^2y and then classify them into relative maxima, relative minima and saddle points.

Q2 - Let f(x,y) = xy - x - y + 3 and R is the triangular region with vertices (0, 0), (2, 0) and (0, 4). Find the interior and boundary points only at which the absolute extrema of f(x,y) can occur.

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: need help urgently...

----

----

which gives stationary points of (0,0) (2,1) (-2,1)

----

forming the hessian matrix:

----  first stationary points (0,0)

-> non degenerate

both eigenvalues are positive, so (0,0) is a local minimum

---- second stationary point (2,1)

-> non degenerate

one eigenvalue is negative, one is positive, so (2,1) is a saddle point

---- third stationary points (-2,1)

-> non degenerate

same eigenvalues as previous stationary point, so (-2,1) is also a saddle point:

--------

(0,0) is a local minimum
(2,1), (-2,1) are saddle points

---

The Beginning Of All Things To End.
The End Of All Things To Come.