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Applications of Derivatives

Maharashtra Board · Class 12 · Mathematics & Statistics -Commerce

Quick revision notes for Applications of Derivatives — Maharashtra Board Class 12 Mathematics & Statistics -Commerce. Key concepts, formulas, and definitions for last-minute revision.

45 questions20 flashcards4 concepts

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Key Topics to Revise

1

Meaning of Derivative and Tangent-Normal

  • Derivative at a point gives the slope of tangent to the curve at that point
  • Tangent line touches the curve at exactly one point locally
  • Normal line is perpendicular to tangent at the point of contact
2

Increasing and Decreasing Functions

  • If f'(x) > 0 in an interval, function is increasing in that interval
  • If f'(x) < 0 in an interval, function is decreasing in that interval
  • Critical points occur where f'(x) = 0 or f'(x) is undefined
3

Maxima and Minima

  • Local maxima occur where f'(x) = 0 and f''(x) < 0
  • Local minima occur where f'(x) = 0 and f''(x) > 0
  • If f''(x) = 0, use higher derivatives or first derivative test
4

Applications in Economics

  • Elasticity of demand measures responsiveness of demand to price changes
  • Marginal revenue relates to average revenue through elasticity
  • Marginal cost shows cost of producing one additional unit

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Full Notes

Key Concepts

The derivative f'(a) at point P(aA function f(x) is increasingLocal maximum occurs at x =Elasticity of demand η =

Frequently Asked Questions

What are the important topics in Applications of Derivatives for Maharashtra Board Class 12 Mathematics & Statistics -Commerce?
Applications of Derivatives covers several key topics that are frequently asked in Maharashtra 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 Applications of Derivatives — Maharashtra Board Class 12 Mathematics & Statistics -Commerce?
Understand the core concepts first, then work through the 45 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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