Derivability on an Interval: Rolle's Theorem

This lecture covers the concept of derivability on an interval, including Rolle's Theorem, finite increments, and Bernoulli-L'Hopital rule. It explains the conditions for a function to be derivable on a closed interval, with examples such as exponential and trigonometric functions. The lecture progresses to discuss the implications of derivability on both sides of a point within an interval, leading to the definition of derivability on a closed interval. It also introduces the concept of right and left derivability at a point within an interval, emphasizing the importance of limits in determining derivability. The lecture concludes with a detailed explanation of Rolle's Theorem and its application in determining specific points within a function.