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