Skip to main content
Super TutorResources
Chapter 2 of 12
Concept Maps

Applications of Differential Calculus — Concept Maps

Tamil Nadu Board · Class 12 · Mathematics

3 concept maps of Applications of Differential Calculus for Tamil Nadu Board Class 12 Mathematics, each also written out as a text outline.

45 questions25 flashcards7 formulas & key relations5 concepts

Interactive on Super Tutor

Studying Applications of Differential Calculus? Get the full interactive chapter.

Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for concept maps and more.

Try Super Tutor — Free

Free trial, no card needed.

3 Concept Maps

Applications of Differential Calculus - Concept Overview

Applications of Differential Calculus - Concept Overview

The map in words

  • Applications of Differential Calculus
    • Meaning of Derivatives
      • Slope of Curve
      • Instantaneous Rate of Change
      • Velocity and Acceleration
      • Related Rates
      • Tangent and Normal Lines
        • Equation of Tangent
        • Equation of Normal
        • Angle Between Curves
    • Mean Value Theorem
      • Rolle's Theorem
      • Lagrange's MVT
      • Monotonicity
      • Critical Points
    • Series Expansions
      • Taylor Series
      • Maclaurin Series
      • Convergence
    • Indeterminate Forms
      • L'Hopital's Rule
      • Form 0/0 and infinity/infinity
      • Exponential Forms
    • First Derivative
      • Monotonicity
      • Increasing Functions
      • Decreasing Functions
      • Local Extrema
      • First Derivative Test
    • Second Derivative
      • Concavity Up/Down
      • Inflection Points
      • Second Derivative Test
    • Optimization
      • Problem Setup
      • Constraint Equations
      • Absolute Extrema
      • Applications
    • Curve Sketching
      • Asymptotes
      • Symmetry
      • Complete Analysis
      • Graph Interpretation

Shows the relationship between secant and tangent slopes, leading to the derivative concept

Shows the relationship between secant and tangent slopes, leading to the derivative concept

The map in words

  • Secant Line Slope
    • As h→0: Tangent Line Slope
      • Derivative f'x
        • Instantaneous Rate: Change at a point
        • Is f'x positive?
          • Yes: Function Increasing
          • No: Function Decreasing
    • Average Rate: Change over interval

Problem-solving strategy for related rates problems

Problem-solving strategy for related rates problems

The map in words

  • Related Quantities
    • Write Constraint Equation
      • Differentiate w.r.t. time
        • Apply Chain Rule
          • Substitute Known Rates
            • Solve for Unknown Rate
              • Interpret Result

Explore these maps interactively

Explore Diagrams

Frequently Asked Questions

What are the important topics in Applications of Differential Calculus for Tamil Nadu Board Class 12 Mathematics?
Key topics in Applications of Differential Calculus include 2 Meaning of Derivatives, 2.4 Tangent and Normal Lines, 3 Mean Value Theorem, 4 Series Expansions. Study these first, then practise questions on each for the Tamil Nadu Board Class 12 board exam.
What do the concept maps for Applications of Differential Calculus show?
The 3 maps show how the ideas in Applications of Differential Calculus connect: Applications of Differential Calculus - Concept Overview; Shows the relationship between secant and tangent slopes, leading to the derivative concept. Each map is also written out as an outline on this page.
How should I revise Applications of Differential Calculus for the Tamil Nadu Board Class 12 board exam?
Learn the core ideas first, then work through the 45 practice questions on Applications of Differential Calculus. 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 Differential Calculus

All Tamil Nadu Board Class 12 Mathematics Concept Maps

For serious students

Get the full Applications of Differential Calculus chapter — start free.

Quizzes, flashcards, an AI doubt solver and a study plan for Tamil Nadu Board Class 12 Mathematics. Free to start, no card needed.

Try Super Tutor Free
Try this chapter free