VCE Specialist Mathematics/Units 3 and 4: Specialist Mathematics/Differential Calculus

Preface
Formal Definition: In mathematics, differential calculus is a subfield of calculus concerned with the study of how functions change when their inputs change. The primary object of study in differential calculus is the derivative. A closely related notion is the differential. The derivative of a function at a chosen input value describes the behavior of the function near that input value. For a real-valued function of a single real variable, the derivative at a point equals the slope of the tangent line to the graph of the function at that point. In general, the derivative of a function at a point determines the best linear approximation to the function at that point.

Translation: Its all about gradients, tangents, normals, finding turning points, and the nature of turning points - fast.