AP Calculus
posted by Sandy on .
Determine whether Rolle's Theorem is valid
f(x) = 3  x  2 for [1, 5]
if so, find c.
if not, tell why.

Rolle's theorem states that:
"Suppose that y=f(x) is continuous at every point of the closed interval [a,b] and differentiable at every point of its interior (a,b). If
f(a)=f(b),
then there is at least one number c in (a,b) at which f'(c)=0.
Here all conditions are satisfied except one. It is not differentiable at x=2, so Rolle's theorem does not apply. Differentiable means that f'(x) exists, but f'(2) is an interior point of (1,5) and f'(2) does not exist. Check the graph below. Post if more help is required.
http://img28.imageshack.us/img28/9139/1297105145.png