TITLE: What is the difference between stationary point and critical point in Calculus?
QUESTION [8 upvotes]: What is the difference between stationary point and critical point? We find critical points by finding the roots of the derivative, but in which cases is a critical point not a stationary point? An example would be most helpful. I am asking this question because I ran into the following question: 

Locate the critical points and identify which critical points are stationary points. 

So, obviously It's implying that not every critical point is a stationary point.

REPLY [5 votes]: All stationary points are critical points but not all critical points are stationary points.
A more accurate definition of the two:
Critical Point:
Let $f$ be defined at $c.$ Then, we have critical point wherever $f '(c)= 0$ or wherever $f(c)$ is not differentiable (or equivalently, $f '(c)$ is not defined).
Points where  $f '(c)$ is not defined are called singular points and points where    $f '(c)$ is 0 are called stationary points. 
Stationary Point: As mentioned above.