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Application of Derivatives

NCERT Class 12 Mathematics Chapter 6

Application of Derivatives for Class 12 Maths and JEE: rates of change, increasing and decreasing functions, and local and absolute maxima and minima.

3 topics Updated 7 Nov 2026

For: Class 12 and JEE

In the syllabus: JEE Class 12 syllabus

With your textbook

NCERT Mathematics Part I (Class 12), Chapter 6 “Application of Derivatives”, reprint 2026-27.

Open the official NCERT chapter (PDF, 3.3 MB, ncert.nic.in)

Checked on 19 Oct 2026.

Learn in this order

  1. Rate of change of quantities

    Rate of change of quantities for Class 12 Maths and JEE: dy/dx as a rate, related rates by the chain rule, marginal cost and revenue, with solved examples.

    NCERT Section 6.2 12 min read 5 solved examples 12 practice questions

  2. Increasing and decreasing functions

    Increasing and decreasing functions for Class 12 Maths and JEE: increasing vs strictly increasing, the sign of f′(x), intervals, with solved examples.

    NCERT Section 6.3 14 min read 5 solved examples 11 practice questions

  3. Maxima and minima

    Maxima and minima for Class 12 Maths and JEE: critical points, first and second derivative tests, local and absolute extrema, applied problems solved.

    NCERT Section 6.4 20 min read 5 solved examples 12 practice questions

Key formulas in this chapter

Rate of change

  • rate of change of y with respect to x = dy/dx
  • dy/dx = (dy/dt)/(dx/dt), for dx/dt ≠ 0
  • marginal cost = dC/dx; marginal revenue = dR/dx

Increasing and decreasing

  • f continuous on [a, b], f′(x) > 0 on (a, b) ⇒ f strictly increasing on [a, b]
  • f continuous on [a, b], f′(x) < 0 on (a, b) ⇒ f strictly decreasing on [a, b]
  • f continuous on [a, b], f′(x) = 0 on (a, b) ⇒ f constant on [a, b]

Maxima and minima

  • critical point: f′(c) = 0 or f′(c) does not exist
  • f′(c) = 0 and f″(c) < 0 ⇒ local maximum
  • f′(c) = 0 and f″(c) > 0 ⇒ local minimum

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