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Applications Of Derivatives - II

ICSE · Class 12 · Mathematics

Practice quiz for Applications Of Derivatives - II — ICSE Class 12 Mathematics. MCQs and questions with answers to test your preparation.

52 questions29 flashcards5 concepts

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A graph of a continuous function on a closed interval [a, b], clearly indicating the absolute maximum and absolute minimum values and their corresponding points.
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Quick Quiz: Applications Of Derivatives - II

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1

The absolute maximum of f on interval I means:

2

A function f has a local minimum at c if:

3

According to the Second Derivative Test, if f'(c) = 0 and f''(c) < 0, then:

4

According to the Second Derivative Test, if f'(c) = 0 and f''(c) > 0, then:

52 Questions·
multiple choicetrue false

Sample Questions

1multiple choice

If f'(c) = 0 and f''(c) = 0, the Second Derivative Test:

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Is inconclusive

When f''(c) = 0, the Second Derivative Test gives no information. Use the First Derivative Test instead.

2multiple choice

The First Derivative Test says: if f' changes from negative to positive at c, then:

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f has a local minimum at c

Negative to positive sign change: function was decreasing then increasing — classic valley (minimum).

3multiple choice

Which of the following is a necessary condition for a local maximum at interior point c?

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f'(c) = 0

Fermat's Theorem: if f has a local extremum at interior c and is differentiable, then f'(c) = 0. This is necessary but NOT sufficient.

4true false

A point c where f'(c) = 0 is always a local maximum or minimum.

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False

False. f(x) = x³ has f'(0) = 0 but x=0 is a point of inflection — neither max nor min.

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Frequently Asked Questions

What are the important topics in Applications Of Derivatives - II for ICSE Class 12 Mathematics?
Key topics in Applications Of Derivatives - II include First Derivative Test, Summary of Tests — Comparison. 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 - II — ICSE Class 12 Mathematics?
Understand the core concepts first, then work through the 52 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.

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