Determine if the requirements for Rolle s theorem are met by the function f x 52 or on the x interval 3 3 If so find the values of cin 3 3 guaranteed by the theorem f x is continuous on 3 3 but not differentiable on 3 3 The conditions of Rolle s theorem are not met f x is not continuous on 3 3 Therefore the first requirement is not met and Rolle s theorem does not apply 5 f x is continuous on 3 3 and differentiable on 3 3 When evaluated f 3 and f 3 5 Therefore f a f b and the conditions of Rolle s theorem are met The value guaranteed by Rolle s theorem is c 0 lo f x is continuous on 3 3 and differentiable on 3 3 When evaluated f 3 55909 5 and f 3 Therefore f a f b and the conditions of Rolle s Theorem are not met