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Revision Notes

Application of Derivatives

Madhya Pradesh Board · Class 12 · Mathematics

Quick revision notes for Application of Derivatives — Madhya Pradesh Board Class 12 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

145 questions60 flashcards5 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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Key Topics to Revise

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.
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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.

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Full Notes

Key Concepts

If y varies with x byMarginal cost is the instantaneous rateA function is increasing if largerA point c in the domainA local maximum is a point

Frequently Asked Questions

What are the important topics in Application of Derivatives for Madhya Pradesh Board Class 12 Mathematics?
Application of Derivatives covers several key topics that are frequently asked in Madhya Pradesh Board Class 12 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Application of Derivatives — Madhya Pradesh Board Class 12 Mathematics?
Understand the core concepts first, then work through the 145 practice questions available for this chapter. Revise formulas and 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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