Rolle's theorem

Rolle's Theorem

	If f(x) is continuous on the interval , if f(a) = f(b) = 0, and if f'(x) exists everywhere on the interval except possibly at the endpoints, then f'(x) = 0 for at least one value of x, say x = xo, between a and b. Geometrically, this means that if a continuous curve intersects the x axis at x = a and x = b, and has a tangent at every point between a and b, then