Question

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

Answer 1

`(0,0), (0, pi/3), (0, (2pi)/3)`......

Explanation:

Find partial derivatives `f_x = 2x, f_y= 3sin3y`
Equating these derivatives to 0, it would be `x=0, y= (n pi)/3`.
n= 0,1,2,....
Critical points would be `(0,0), (0, pi/3), (0, (2pi)/3)`......