Introduction to Continuity Types of Discontinuity: removable, jump, and infinite discontinuities Algebra of Continuous Functions: properties of algebraic operations on continuous functions Intermediate Value Theorem: application in determining the existence of roots and solutions Differentiability and its Relation to continuity Derivatives and their interpretation in terms of rates of change Relationship between differentiability and continuity of functions Rolle's Theorem and its application in finding points of vanishing derivatives Mean Value Theorem and its application in finding points with equal average and instantaneous rates of change Analysis of increasing and decreasing functions using derivatives Application of derivatives in optimization problems: finding maximum and minimum values Tangents and Normals: equations of tangent and normal lines to a curve using derivatives.
