How does Rolle's theorem differ from the mean value theorem?

Rolle's theorem states that for a continuous real valued
function f(x) in a closed interval  (a, b) and differentiable in the open interval
(a,b), b> a with f(a) = f(b) , there exists a point c where f'(c) =
0.

The mean value theorem states that for a continuous real
valued function f(x) in the closed interval (a,b), and differentiablen the open interval
(a,b), b > a there exists a point c in (a,b)  for
which

f'(c) =
(f(b)-f(a))/(b-a).

If we examine both theorems, it looks
Rolle's theorem is a special case of mean value
theorem. 

In Rolle's f(a) = f(b) . In mean value theorem
f(a) and f(b) are not equal. 

In rolle's theorem f'(c) = 0
. The curve has a tangent || to x axis.

In the mean value
theorem the slope f'(c) is not zero. f'(c) is the slope of the tangent at the point c
and this tangent is not parallel to x axis. But this tangent is || to the line joining
(a , f(a) ) and the point (b , f(b)) the end points of the
curve.

Hope this helps.