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DanielHendrycks
Show (0,0) is a saddle point of the function 2x^3 + 6xy + 3y^2
My second derivative test failed since it equaled 0, so I am not certain how to proceed.
Can you show what you did for the second derivative test? My second derivative test shows "AC-B^2" to be negative, which is indeed indicative of a saddle point.
\[12x\cdot6-[6(x^2+y)\cdot6(x+y)]^2=12\cdot0\cdot6-[6(0+0)\cdot6(0+0)]^2=0\]
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.