Wyznaczyc ekstrema lokalne

[Darekstalowka]

\(\displaystyle{ f(x,y)=xe^{y ^{2}- x^{2}}=e^{lnx}\cdot e^{y^2-x^2}=e^{lnx+y^2-x^2} \\
\frac{\partial f}{\partial x}=
e^{lnx+y^2-x^2}\cdot (lnx+y^2-x^2)'_x=
e^{lnx+y^2-x^2}\cdot (\frac{1}{x}-2x)\\
\frac{\partial f}{\partial y}=
e^{lnx+y^2-x^2}\cdot (lnx+y^2-x^2)'_y=
e^{lnx+y^2-x^2}\cdot (2y)}\)

[soku11]

\(\displaystyle{ \begin{cases} \frac{1}{x}-2x=0\\2y=0\end{cases}\\
\begin{cases} 1-2x^2=0\\y=0\end{cases}\\
\begin{cases} (1-\sqrt{2}x)(1+\sqrt{2}x)=0\\y=0\end{cases}\\
A=\left(\frac{\sqrt{2}}{2},0\right)\ \ B=\left(-\frac{\sqrt{2}}{2},0\right)}\)

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