Question

is critical point/points opposite to continuous/continuity of a function?

Answer 1

critical points show where there are maximum and minimum.
Continuous just means the function is continous.
If you can show the derivative at a point, then you can say at that point the function is continuous.

Answer 2

Definition of a Critical point
An interior point c of the domian of f at which f prime of c is equal to zero or f prime of c fails to exist is called a critical point of f.

Answer 3

thanks