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Applications Of Derivatives - II — Revision Notes

ICSE · Class 12 · Mathematics

Applications Of Derivatives - II revision notes for ICSE Class 12 Mathematics: 4 topics in quick points. Part of the ICSE Class 12 Mathematics syllabus.

52 questions29 flashcards10 formulas & key relations5 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

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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.
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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.
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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.
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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 Absolute Maximum, Absolute Minimum, and Absolute Extremum, Critical Points, Stationary Points, and Inflexion, First Derivative Test, Second Derivative Test. Study these first, then practise questions on each for the ICSE Class 12 board exam.
How should I revise Applications Of Derivatives - II for the ICSE Class 12 board exam?
Learn the core ideas first, then work through the 52 practice questions on Applications Of Derivatives - II. 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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