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Formula Sheet

Applications of Derivatives - I

ICSE · Class 12 · Mathematics

All formulas from Applications of Derivatives - I in ICSE Class 12 Mathematics. Key equations, constants, and identities for board exam preparation.

55 questions37 flashcards5 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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18 Formulas · 4 Sections

Formulas

1. Rate of Change of Quantities

Average rate of change = (Δy)/(Δx)

Instantaneous rate of change = dy/dx = lim(Δx→0) (Δy)/(Δx)

dy/dx = (d y/d x) = f'(x)

2. Approximation by Differentials

Δy ≈ (dy/dx)Δx

Absolute error in x = Δx

Absolute error in y = Δy

Relative error in x = Δx/x

Percentage error in x = (Δx/x × 100)%

3. Increasing and Decreasing Functions

Strictly increasing on I: x1 < x2 ⇒ f(x1) < f(x2)

Increasing on I: x1 < x2 ⇒ f(x1) ≤ f(x2)

Strictly decreasing on I: x1 < x2 ⇒ f(x1) > f(x2)

Decreasing on I: x1 < x2 ⇒ f(x1) ≥ f(x2)

Theorem 12.1: f'(x) > 0 ⇒ f is strictly increasing

4. Tangent and Normal to a Curve

Slope of tangent at (a, f(a)) = (dy/dx) at x=a

Tangent equation: y - β = (dy/dx)_(α,β) (x - α)

Slope of normal = -1 / (dy/dx)_(α,β)

Normal equation: y - β = -1/(dy/dx)_(α,β) (x - α)

Slope of line through two points: m = (y2 - y1)/(x2 - x1)

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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 First Derivative Test for Monotonicity, Important Geometric Problems. 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 - I — ICSE Class 12 Mathematics?
Understand the core concepts first, then work through the 55 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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