# What are the critical points of  f(x,y)=x^3 y + 4x^2 − 8y?

Nov 14, 2016

$\left(2 , - \frac{4}{3}\right)$

#### Explanation:

${f}_{x} \left(x , y\right) = 3 {x}^{2} y + 8 x$

${f}_{y} \left(x , y\right) = {x}^{3} - 8$

Solve:
$3 {x}^{2} y + 8 x = 0$

${x}^{3} - 8 = 0$ $\text{ }$ so $x = 2$ now substitute in the other equation to get

$12 y + 16 = 0$ $\text{ }$ so $y = - \frac{4}{3}$