Which version of Rolle's theorem is correct? #According to my textbook:
Rolle's theorem states that if a function $f$ is continuous on the closed interval $[a, b]$ and differentiable on the open interval $(a, b)$ such that $f(a) = f(b)$, then $f′(x) = 0$ for some $x$ with $a ≤ x ≤ b$.
#According to Wikipedia:
If a real-valued function $f$ is continuous on a proper closed interval $[a, b]$, differentiable on the open interval $(a, b)$, and $f(a) = f(b)$, then there exists at least one $c$ in the open interval (a, b) such that
$f'(c)=0$.
So one definition says that $c$ should belong in closed interval $[a,b]$ but the other says that $c$ should be in open interval $(a,b)$.
Which definition is correct ? Why?

It would most likely be wikipedia, but for small things like this it doesnt really matter. If you are tested, just follow your textbook.
Wikipedia logic:
$$f(x) = 4-x^2$$
f is continuous on $[-2,2]$
f is differential on $(-2,2)$
$f'(c) = 0 \to  x = 0$
and $ x \in (-2,2)/[-2,2] $
Thus both are valid, but as you can see, the $0$ is more valid inside the interval (wikipedia)
