When are rolle's theorem and the mean value theorem equivalent?

For a function  : for the secant line in the mean value theorem, if you choose an interval  (where is continuous on , differentiable on   such that  , then the mean value theorem and rolle's theorem are equivalent.if , the secant line will have a slope of 0, which agrees with rolle's theorem. for rolle's theorem: there will be at least one number  in such that  .for mean value theorem: there will be at least one number  in such that