Timeless Theorems of Mathematics/Rolle's Theorem

The Rolle's theorem says that, If a real-valued function is continuous on a closed interval , differentiable on an open interval and , then there exists at least a number such that . It means that if a function satisfies the three conditions mentioned in the previous sentence, then there is at least a point in the graph of the function, where the slope of the tangent line at the point is , or the tangent line is parallel to the -axis. Proof thumb|f(x) is continuous on differentiable on and . Thus, 25%