Question: (a) Given \(f:\mathbb{R}\to \mathbb{R}\), prove that differentiability implies continuity, but not vice versa.

(b) Consider an interval \(I\subset \mathbb{R}\) and suppose that \(f:I\to \mathbb{R}\) is continuous. Prove that if (i) x* is a local maximum of f and (ii) x* is the only extreme point of f on I, then x* is the only global maximum.