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Applications Of Derivatives - II — Practice Quiz

ICSE · Class 12 · Mathematics

Try a 4-question quiz on Applications Of Derivatives - II for ICSE Class 12 Mathematics: tap an answer to check it and see why.

52 questions29 flashcards10 formulas & key relations5 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.

+48 more questions on Applications Of Derivatives - II (ICSE Class 12 Mathematics)

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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 Absolute Maximum, Absolute Minimum, and Absolute Extremum, Critical Points, Stationary Points, and Inflexion, First Derivative Test, Second Derivative Test. Study these first, then practise questions on each for the ICSE Class 12 board exam.
How many practice questions are there for Applications Of Derivatives - II?
There are 52 questions on Applications Of Derivatives - II. Try the 4-question sample quiz on this page first; each answer shows an explanation when you tap it.

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