# What are the critical points of  f(x,y) = 1 + x^2 - cos(3y)?

$\left(0 , 0\right) , \left(0 , \frac{\pi}{3}\right) , \left(0 , \frac{2 \pi}{3}\right)$......
Find partial derivatives ${f}_{x} = 2 x , {f}_{y} = 3 \sin 3 y$
Equating these derivatives to 0, it would be $x = 0 , y = \frac{n \pi}{3}$.
Critical points would be $\left(0 , 0\right) , \left(0 , \frac{\pi}{3}\right) , \left(0 , \frac{2 \pi}{3}\right)$......