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Applications Of Derivatives - II

ICSE · Class 12 · Mathematics

Quick revision notes for Applications Of Derivatives - II — ICSE Class 12 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

52 questions29 flashcards5 concepts

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A graph of a continuous function on a closed interval [a, b], clearly indicating the absolute maximum and absolute minimum values and their corresponding points.
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Key Topics to Revise

1

1. Absolute Maximum, Absolute Minimum, and Absolute Extremum

  • Absolute maximum is the greatest value of a function on an interval.
  • Absolute minimum is the least value of a function on an interval.
  • Absolute extremum means either the maximum value or the minimum value.
2

2. Critical Points, Stationary Points, and Inflexion

  • Stationary points or turning points are the values of x for which f'(x) = 0.
  • Critical points are the values of x for which f'(x) = 0 or f'(x) does not exist.
  • Every stationary point is a critical point, but not every critical point is stationary.
3

3. First Derivative Test

  • If f'(x) changes from positive to negative at c, then f has a local maximum at c.
  • If f'(x) changes from negative to positive at c, then f has a local minimum at c.
  • If f'(x) keeps the same sign on both sides of c, then c is a point of inflexion.
4

4. Second Derivative Test

  • If f'(c) = 0 and f''(c) < 0, then f has a local maximum at c.
  • If f'(c) = 0 and f''(c) > 0, then f has a local minimum at c.
  • If f'(c) = 0 and f''(c) = 0, no conclusion comes from the second derivative test.

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Full Notes

Key Concepts

Absolute maximum is the greatest valueA local maximum is greater thanStationary points are values where f'(x)=0If f'(x) changes from positiveIf f'(c)=0 and f''(c)<0

Frequently Asked Questions

What are the important topics in Applications Of Derivatives - II for ICSE Class 12 Mathematics?
Key topics in Applications Of Derivatives - II include First Derivative Test, Summary of Tests — Comparison. These are the concepts ICSE Class 12 examiners draw on most — study them first, then practise related questions.
How to score full marks in Applications Of Derivatives - II — ICSE Class 12 Mathematics?
Understand the core concepts first, then work through the 52 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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