saddle points

**amandaishere** · December 3rd 2007, 01:56 AM

thank you

**tukeywilliams** · December 3rd 2007, 02:21 AM

Remember that $D = \det \begin{bmatrix} f_{xx}&f_{xy} \\ f_{yx}&f_{yy} \end{bmatrix}$ .

If $D > 0, \ f_{xx} > 0$ then we have a minimum. If $D > 0, \ f_{xx} < 0$ then we have a maximum. If $D < 0$ then we have a saddle point.

**amandaishere** · December 3rd 2007, 02:26 AM

still a bit confused by this

**tukeywilliams** · December 3rd 2007, 02:30 AM

$f_x = 3x^2-3y = 0$
$f_y = -3y^2-3x = 0$

Now solve for $(x,y)$ such that the above holds. $(0,0)$ is a critical point. $(-1,1)$ is also CP.

**amandaishere** · December 3rd 2007, 02:36 AM

would you be able tos how me a step by step on how to get from question to the answer so I no for future questions please?

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