Finding critical points of a parent function

Question

How do we know that the function y=x has critical points of (1,1) (-1,-1) and (0,0)?

Answer 1

take the derivative, and set = 0, solve for x

f'(x) = 2x = 0, x=0, also any values of x that make f'(x) undefined but there are none

f(0) = 0^2 = 0

(0,0) is the critical point, an inflection point where concavity changes, concave downward to upward