Sue is a runner. At time t = 0 she runs down a steep hill, turns around and runs back up it. At time t = 1 she is in the same place she started. Assume that her elevation (let the bottom of the hill be elevation 0), is f(x) = x 0.5], [0, 1]. Can Rolle's Theorem be applied to show that at some point between t = 0 and t = 1, Sue has achieved a maximum and/or minimum speed? The conditions of Rolle's Theorem are met and Rolle's Theorem does state that you can find min or max points. The conditions of Rolle's Theorem are not met. The conditions of Rolle's Theorem are not met but Rolle's Theorem does not state that you can find min or max points. The conditions of Rolle's Theorem are met and Rolle's Theorem does not state that you can find min or max points.