Question

Ache os pontos críticos da função f(x , y)=2x^4+y^2-x^2-2y.

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Answer 1

$f(x , y)=2x^4+y^2-x^2-2y$

Derivadas parciales

$\frac{\partial f}{\partial x}=8x^3-2x=0\Longrightarrow x\in\left\{-\frac{1}{2},0,\frac{1}{2}\right\}$

$\frac{\partial f}{\partial y}=2y-2=0\Longrightarrow y=1$

Entonces los puntos críticos son

$\left(-\frac{1}{2},x_1\right) ; \left(\frac{1}{2},x_2\right);\left(2,x_3\right) \mbox{ y } (y_1,1)$

donde

$x_1,x_2,x_3 \mbox{ y } y_1 \in \mathbb R$