# Find Critical point and nature f(x,y)=(x^2+y^2)^2−2x^2+2y^2 So (del)/(delx)f(x,y)=4x(x^2+y^2)−4x (del)/(del)yf(x,y)=4y(x^2+y^2)+4y

Find Critical point and nature
$4x\left({x}^{2}+{y}^{2}-1\right)=0$
$4y\left({x}^{2}+{y}^{2}+1\right)=0$
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Evelin Castillo
From the second equation, $y=0$. That's because
${x}^{2}+{y}^{2}+1\ge 1$
for any real $x$ and $y$. So than either $x=0$ or ${x}^{2}-1=0$. So the critical points are $\left(0,0\right)$, $\left(-1,0\right)$, and $\left(1,0\right)$.