Master Applications of Derivatives – Class 12 Maths Chapter 6 | Tangents, Max‑Min, Approximation, NCERT & PYQs
Here's the complete guide to Chapter 6: Applications of Derivatives (Class 12 CBSE Maths, 2025–26 syllabus): 🧠A. Key Concepts & Applications Rate of Change The derivative d y / d x dy/dx represents the rate at which y y changes w.r.t. x x . Applicable in physics (velocity, acceleration), economics (marginal cost/revenue), biology, etc. Tangents and Normals Slope of tangent at x = a x = a : m = f ′ ( a ) m = f'(a) . Equation of tangent: y − f ( a ) = f ′ ( a ) ( x − a ) y - f(a) = f'(a)(x - a) . Normal line slope: − 1 / f ′ ( a ) -1/f'(a) . Increasing/Decreasing Functions & Stationary Points If f ′ ( x ) > 0 f'(x) > 0 → increasing; f ′ ( x ) < 0 f'(x) < 0 → decreasing. Stationary points where f ′ ( x ) = 0 f'(x) = 0 . Test using sign of f ′ ( x ) f'(x) or second derivative f ′ ′ ( x ) f''(x) (if > 0 >0 : min, if < 0 <0 : max). Maxima and Minima Locally highes...