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Roll's Theorem 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 between a and b at which f'(c) = 0.
The Mean Value Theorem If y=f(x) is continuous at every point of the closed interval[a,b] and differentiable at every point of its interior(a,b), then there is at least one number c between a and b at which f'(c)(b-a) = f(b)-f(a)