Class 12 Mathematics Chapter 6 Applications of Derivatives – Revision Notes

Quick revision notes for Class 12 Maths Chapter 6 (Applications of Derivatives). These Class 12 Mathematics Chapter 6 notes are ideal for quick revision just before exams.

Key Concepts

• Rate of change: dy/dx as instantaneous rate.
• Increasing: f'(x)≥0; decreasing: f'(x)≤0.
• Tangent: y−y₀=f'(x₀)(x−x₀); Normal slope=−1/f'(x₀).

Approximation & Extrema

• Δy≈f'(x)Δx (differentials).
• Critical points: f'(x)=0.
• Second derivative test: f”<0 ⇒ local max; f”>0 ⇒ local min.
• Absolute extrema on [a,b]: compare critical points and endpoints.

One-Line Summary

Derivatives model rates of change, define tangents/normals, and identify increasing/decreasing behaviour and local/absolute extrema via first and second derivative tests.

Written by Satish

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