Question

Is there a deviation of standard definitions in 18.01 Single Variable Calculus lectures by professor Jerison?

I have always been taught that critical points of f(x) are stationary points of f(x) + points where f(x) is not defined.

Prof Jerison does not introduce stationary points but rather defines critical points of f(x) such that f'(x) = 0. Ie this comes to him saying that

y = (x+1)/(x+2) does not have critical points.

Which notation is more appropriate?

Answer 1

Spivak defines a critical point the same way, as a number x such that f'(x)=0. I think generally it is said that points where f'(x)=0 are critical points, while points where f'(x) is undefined are just 'also points to look into.'

Answer 2

Then again, wikipedia says that a point where a function is not differentiable is considered a critical point, so I guess both definitions are in common use.