Question

find stationary points and examine for max & min.
f(x,y)=x^2+y^2+3xy

Answer 1

@ganeshie8 @hartnn @wio @Directrix @nubeer can u help her

Answer 2

You need to find the gradient first,
\[\nabla f(x,y)=(2x+3y,2y+3x)\]Then, find the candidate points,
\[\nabla f(x,y)=(2x+3y,2y+3x)=(0,0)\Rightarrow(x,y)=(0,0)\]Now, you must find which type of point you have. You need the Hessian (may be you can use another criteria),
\[H(x,y)=\left(\begin{matrix} \frac{\partial^2 f}{\partial x^2} & \frac{\partial^2 f}{\partial x\partial y} \\ \frac{\partial^2 f}{\partial y\partial x} & \frac{\partial^2 f}{\partial y^2}\end{matrix}\right)=\left(\begin{matrix} 2 & 3 \\ 3& 2\end{matrix}\right)\] Use the Sylvester cryteria, and you will find that you have a saddle point in (0,0) but no maxima or minima.

Answer 3

okay thank u sooo mch!

Answer 4

;)