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Applications Of Derivatives - II — Concept Maps

ICSE · Class 12 · Mathematics

3 concept maps of Applications Of Derivatives - II for ICSE Class 12 Mathematics, each also written out as a text outline.

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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One of 4 illustrations for Applications Of Derivatives - II in Super Tutor — alongside flashcards, concept maps and practice questions.

3 Concept Maps

First Derivative Test

First Derivative Test

The map in words

  • Critical point c
    • Test f' just LEFT of c
      • f' left = ?
        • Positive (+): +
          • Combined
            • + then -: LOCAL MAX
            • - then +: LOCAL MIN
            • same sign: INFLECTION
        • Negative (-): -
    • Test f' just RIGHT of c
      • f' right = ?
        • Positive (+): +
        • Negative (-): -

Summary of Tests — Comparison

Summary of Tests — Comparison

The map in words

  • Find extrema of f
    • Closed interval?
      • Yes: Closed Interval Method\nCompare f at critical pts + endpoints
      • No: Find critical points: f'=0
        • Compute f'' at each critical pt
          • f''(c) ≠ 0?
            • f''<0: LOCAL MAX
            • f''>0: LOCAL MIN
            • f''=0: Use 1st Derivative Test\nSign chart of f

Maxima, minima, and optimization using derivatives

Maxima, minima, and optimization using derivatives

The map in words

  • Maxima, minima, and optimization using derivatives
    • Absolute maximum
    • Absolute minimum
    • Absolute extremum
    • Local maxima
    • Local minima
    • Stationary points
    • Critical points
    • Point of inflexion

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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.
What do the concept maps for Applications Of Derivatives - II show?
The 3 maps show how the ideas in Applications Of Derivatives - II connect: First Derivative Test; Summary of Tests — Comparison. Each map is also written out as an outline on this page.
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.

More resources for Applications Of Derivatives - II

All ICSE Class 12 Mathematics Concept Maps

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