Timeless Theorems of Mathematics/Rolle's Theorem

The Rolle's theorem says that, If a real-valued function $$f$$ is continuous on a closed interval $$[a, b]$$, differentiable on an open interval $$(a, b)$$ and $$f(a) = f(b)$$, then there exists at least a number $$c$$ such that $$D_xf(c) = 0$$. 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 $$0$$, or the tangent line is parallel to the $$x$$-axis.