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Syllabus

Application of Derivatives — Syllabus

Madhya Pradesh Board · Class 12 · Mathematics

What Application of Derivatives covers in Madhya Pradesh Board Class 12 Mathematics: 4 topics, for the 2026-27 session.

145 questions60 flashcards18 formulas & key relations5 concepts

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An infographic explaining the concept of a derivative as the instantaneous rate of change of one quantity with respect to another, using a simple example like distance vs. time.
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4 Topics · Madhya Pradesh Board Class 12 Mathematics · 2026-27

Topics in Application of Derivatives

1

1. Rate of Change of Quantities

  • A derivative gives the rate of change of one quantity with respect to another.
  • If a quantity y varies with x by a rule y = f(x), then dy/dx represents the rate of change of y with respect to x.
  • If x and y both vary with another variable t, then dy/dx can be found using the chain rule.
2

2. Increasing and Decreasing Functions

  • A function can be increasing, decreasing, constant, strictly increasing, or strictly decreasing on an interval.
  • Increasing means larger x gives larger or equal function values.
  • Decreasing means larger x gives smaller or equal function values.
3

3. Local Maxima, Local Minima, and Critical Points

  • A local maximum is a point where the function value is greatest in some small neighbourhood.
  • A local minimum is a point where the function value is smallest in some small neighbourhood.
  • Local extrema are different from absolute extrema.
4

4. Absolute Maximum and Minimum on a Closed Interval

  • A continuous function on a closed interval has both an absolute maximum and an absolute minimum.
  • Absolute maximum and absolute minimum are different from local extrema.
  • To find absolute extrema on a closed interval, check critical points and endpoints.

Key Concepts

Central concept: Application of Derivatives

Rate of change of quantitiesIncreasing and decreasing functionsLocal maxima and local minimaTests for extremaAbsolute maximum and absolute minimumApplications in geometry and optimisationApplications in economicsRelated rates problems

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Frequently Asked Questions

What are the important topics in Application of Derivatives for Madhya Pradesh Board Class 12 Mathematics?
Key topics in Application of Derivatives include Rate of Change of Quantities, Increasing and Decreasing Functions, Local Maxima, Local Minima, and Critical Points, Absolute Maximum and Minimum on a Closed Interval. Study these first, then practise questions on each for the Madhya Pradesh Board Class 12 board exam.
How should I revise Application of Derivatives for the Madhya Pradesh Board Class 12 board exam?
Learn the core ideas first, then work through the 145 practice questions on Application of Derivatives. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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All Madhya Pradesh Board Class 12 Mathematics Syllabus

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