Mathematics Asked by Mads Peter Balle on December 6, 2020

Find all stationary pointsfor function

$$f(x,y)=3y^3-x^3-2y^2+4x-2y.$$

So far this is what I have

$$frac{partial f}{partial x}left(3y^3-x^3-2y^2+4x-2yright)=-3x^2-4$$ and

$$frac{partial f}{partial y}left(3y^3-x^3-2y^2+4x-2yright)=9y^2-4y-2$$

What do I do from here? I know it’s somthing along the lines of making them equal to $0$.

You wrote

$frac{partial f}{partial x}left(3y^3-x^3-2y^2+4x-2yright)=-3x^2-4$

but it should read

$frac{partial f}{partial x}left(3y^3-x^3-2y^2+4x-2yright)=-3x^2+4.$

If $x_0$ is such that $-3x_0^2+4=0$ and if $y_0$ is such that $9y_0^2-4y_0-2=0$,

then $(x_0,y_0)$ is a stationary point of $f.$

Answered by Fred on December 6, 2020

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