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

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

WaynexBest ResponseYou've already chosen the best response.2
Can 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.
 one year ago

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

WaynexBest ResponseYou've already chosen the best response.2
It 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.
 one year ago
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