Derivability and Extrema Analysis

This lecture discusses the concept of derivability at a specific point, focusing on the case where the function is not differentiable. The instructor demonstrates how to analyze points of non-differentiability using definitions and calculations of left and right limits. The lecture also covers finding local extrema by examining points where the derivative is zero and evaluating the function at the boundaries of the interval. Through detailed mathematical reasoning, the instructor illustrates how to determine local minima and maxima, ultimately establishing the image of the function as the interval [-3, 3].