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DanielHendrycks
 2 years ago
Show (0,0) is a saddle point of the function 2x^3 + 6xy + 3y^2
DanielHendrycks
 2 years ago
Show (0,0) is a saddle point of the function 2x^3 + 6xy + 3y^2

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DanielHendrycks
 2 years ago
Best ResponseYou've already chosen the best response.0My second derivative test failed since it equaled 0, so I am not certain how to proceed.

Waynex
 2 years ago
Best ResponseYou've already chosen the best response.2Can you show what you did for the second derivative test? My second derivative test shows "ACB^2" to be negative, which is indeed indicative of a saddle point.

DanielHendrycks
 2 years ago
Best ResponseYou've already chosen the best response.0\[12x\cdot6[6(x^2+y)\cdot6(x+y)]^2=12\cdot0\cdot6[6(0+0)\cdot6(0+0)]^2=0\]

Waynex
 2 years ago
Best ResponseYou've already chosen the best response.2It looks like you took did this:\[F _{xx}*F _{yy}[F _{x}*F _{y}]^{2}.\]What you need to do is this:\[F _{xx}*F _{yy}(F _{xy})^{2}.\]Notice that the last part there is the second derivative with respect to x and y. You took the first derivative with respect to x and multiplied by the first derivative with respect to y.
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