IITJEE Advance • Mathematics New Syllabus
Module 08: Application of Derivatives Hub
Master the geometrical and physical interpretations of derivatives. Explore monotonicity, tangents and normals, mean value theorems, and advanced optimization (maxima and minima) problems.
Topic 1.1 • Curve Geometry
Equations of Tangent and Normal, Angle of Intersection, and Orthogonal Curves
Topic 1.2 • Physical Interpretation
Derivative as a Rate of Change, Related Rates, and Differentials for Approximations
Topic 2.1 • Function Behavior
Increasing and Decreasing Functions, Strict Monotonicity, and Critical Points Analysis
Topic 2.2 • Essential Theorems
Rolle’s Theorem, Lagrange’s Mean Value Theorem (LMVT), and their Geometrical Significance
Topic 3.1 • Local Optima
First and Second Derivative Tests for Local Maxima/Minima, and Points of Inflection
Topic 3.2 • Global Extrema
Global Maxima & Minima in Closed/Open Intervals, and Greatest/Least Values
Topic 4.1 • Word Problems
Geometrical and Practical Optimization Problems on Maximization and Minimization
Topic 4.2 • Advanced AOD