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Applications of Derivatives - I — Formula Sheet

ICSE · Class 12 · Mathematics

23 formulas from Applications of Derivatives - I (ICSE Class 12 Mathematics) on one page, grouped by topic. Part of the ICSE Class 12 Mathematics syllabus.

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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23 Entries · 8 Sections

Formulas and Key Relations

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)

Rate of Change and Differentials

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

Increasing and Decreasing Functions

Increasing means x1 < x2 implies f(x1) ≤ f(x2).

Tangent and Normal to a Curve

dy/dx at x = a gives the slope of the tangent to y = f(x) at (a, f(a)).

For small Δx, Δy ≈ (dy/dx)Δx.

Percentage error = relative error × 100%.

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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.
How many formulas are in Applications of Derivatives - I?
This sheet lists 23 formulas from Applications of Derivatives - I, grouped by topic. Learn what each symbol stands for so you can apply the formula, not just recall it.
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 Formula Sheet

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