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Applications of Derivatives - I — Concept Maps

ICSE · Class 12 · Mathematics

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

55 questions37 flashcards23 formulas & key relations5 concepts

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A graph of a function y=f(x) with a tangent line at a point (x, y), illustrating dy/dx as the slope of the tangent.
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3 Concept Maps

First Derivative Test for Monotonicity

First Derivative Test for Monotonicity

The map in words

  • Find f'(x)
    • Solve f'(x) = 0\nGet critical points
      • Number line with critical points
        • Test f' sign in each interval
          • f'(x) > 0?
            • Yes: INCREASING ↑
            • No: DECREASING ↓

Important Geometric Problems

Important Geometric Problems

The map in words

  • Condition on tangent
    • Type?
      • Slope = m given: Solve f'(x) = m
        • Find x, then y = f(x)
      • Parallel to line: Slope of line = -a/b\nSolve f'(x) = -a/b
      • Passes through (h,k): Write tangent at (t,f(t))\nSubstitute (h,k), solve for t

Applications of derivatives in rate of change, approximation, monotonicity, tangents, normals, and angle of intersection

Applications of derivatives in rate of change, approximation, monotonicity, tangents, normals, and angle of intersection

The map in words

  • Applications of derivatives in rate of change, approximation, monotonicity, tangents, normals, and angle of intersection
    • Rate of Change of Quantities
    • Approximation by Differentials
    • Increasing and Decreasing Functions
    • Tangent and Normal to a Curve
    • Angle of Intersection of Curves
    • Logarithmic Function Monotonicity
    • Worked Applications and Standard Question Types

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Frequently Asked Questions

What are the important topics in Applications of Derivatives - I for ICSE Class 12 Mathematics?
Key topics in Applications of Derivatives - I include Rate of Change and Differentials, Approximation by Differentials, Increasing and Decreasing Functions, Tangent and Normal to a Curve. Study these first, then practise questions on each for the ICSE Class 12 board exam.
What do the concept maps for Applications of Derivatives - I show?
The 3 maps show how the ideas in Applications of Derivatives - I connect: First Derivative Test for Monotonicity; Important Geometric Problems. Each map is also written out as an outline on this page.
How should I revise Applications of Derivatives - I for the ICSE Class 12 board exam?
Learn the core ideas first, then work through the 55 practice questions on Applications of Derivatives - I. 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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All ICSE Class 12 Mathematics Concept Maps

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