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?

In both the theorams 2 things are common
1.) Function is continuous on $\left[a,b\right]$
2.) function is differentiable on $\left(a,b\right)$$\Longrightarrow$may be or may not be differentiable at x=a and x=b.
Case 1. 
$\Longrightarrow$function is differentiable at x=a and x=b
Both theorams are correct
Case 2. 
$\Longrightarrow$function is not differentiable at x=a and x=b
textbook theoram becomes improper.Where wikipidea theoram is still
correct
