I was reading this - https://en.wikipedia.org/wiki/Stationary_point and got stuck comprehending meaning of this sentence.
Particularly, I'm having trouble with "projection parallel to the x-axis". I tried reading https://en.wikipedia.org/wiki/Parallel_projection but that page seems tangential to the meaning in context.
Can you kindly help?
That paragraph is indeed confusing. I will edit it.
What the paragraph is trying to say is that most authors use "stationary point" of a one-variable real-valued function to refer to a a point where the tangent line is horizontal (parallel to the $x$ axis). But one might also be interested in cases where the tangent line is vertical (parallel to the $y$ axis). Many authors use "critical point" to refer to either case.
This amounts to saying that a critical point is a point where $f'$ is zero or undefined, while a stationary point is a point where $f'$ is zero.
So $f(x)=x^2$ has a stationary point (thus also a critical point) at the origin, but $f(x)=x^{1/3}$ has a critical point (but not a stationary point) at the origin.
That, at least, is what the paragraph means. I'm not sure this distinction is held to very rigidly. You should just be careful to use whatever definition your book or teacher or the paper you're reading uses.
