CBSE · Class 12 · Mathematics · Chapter 6

Application of Derivatives

Applications of derivatives in real-life problems.

7 lessons 120 min
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Lessons in this chapter

  1. 1Rates of Change in Real SituationsTranslate changing quantities into derivatives and interpret related rates with correct signs and units.
  2. 2Increasing and Decreasing FunctionsUse derivative signs and interval reasoning to explain where a function rises, falls, or stays constant.
  3. 3Understanding Maximum and Minimum ValuesDistinguish local and absolute extrema, recognise the role of the domain, and identify critical candidates.
  4. 4Testing for Local ExtremaClassify critical points using derivative signs and choose a valid test when a shortcut is inconclusive.
  5. 5Building and Solving Optimization ModelsBuild a one-variable objective from constraints and justify the greatest or least feasible outcome.
  6. 6Absolute Extrema on Closed IntervalsFind greatest and least values by comparing critical inputs and endpoints, while checking existence and domain conditions.
  7. 7Chapter Summary and PracticeConnect every chapter method and choose a justified approach for mixed rate, monotonicity, and optimization problems.
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