Differential Calculus - UJ

Functions & Limits: Reviewing algebraic, trigonometric, exponential, and logarithmic functions while defining their domains and ranges. This section establishes the rigorous definition of a limit (\(\lim_{x \to a} f(x) = L\)) and determines structural continuity.The Derivative: Introducing the derivative as the slope of a tangent line and a instantaneous rate of change.Differentiation Rules: Mastering fundamental rules such as the Product Rule, Quotient Rule, Chain Rule, and Implicit Differentiation.Applications of Derivatives: Using the first and second derivatives to locate local/absolute extrema, intervals of increase/decrease, concavity, and points of inflection. This concludes with solving structural optimization problems.