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Applications of Derivatives - I — Important Questions

ICSE · Class 12 · Mathematics

55 important questions from Applications of Derivatives - I for ICSE Class 12 Mathematics, with answers. Includes multiple choice and true false questions.

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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55 Questions·
multiple choicetrue false

Important Questions from Applications of Derivatives - I

1multiple choice

The approximate change in y = f(x) for a small change Δx in x is:

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f'(x)·Δx

Δy ≈ dy = f'(x)·Δx. The differential dy is the approximate change in y.

2multiple choice

For f(x) = √x and x = 25, Δx = 0.5, the approximate value of √25.5 is:

Show answer

5.05

f(x)=√x, f'(x)=1/(2√x)=0.1 at x=25. f(25.5)≈5+0.1×0.5=5+0.05=5.05.

3multiple choice

A function f is strictly increasing on interval I if:

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x₁ < x₂ ⟹ f(x₁) < f(x₂) for all x₁,x₂ ∈ I

Strictly increasing means a larger x always gives a strictly larger f(x).

4multiple choice

If f'(x) < 0 for all x ∈ (a,b), then f is:

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Strictly decreasing on (a,b)

f'(x) < 0 means the function is falling — it is strictly decreasing.

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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 important questions are there in Applications of Derivatives - I?
Super Tutor has 55 practice questions for Applications of Derivatives - I, including multiple choice, true false questions. A sample with answers is on this page.

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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 Important Questions

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