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Applications Of Derivatives - II — Formula Sheet

ICSE · Class 12 · Mathematics

10 formulas from Applications Of Derivatives - II (ICSE Class 12 Mathematics) on one page, grouped by topic. Covers Absolute Maximum, Absolute Minimum.

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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10 Entries · 5 Sections

Formulas and Key Relations

2. Absolute Maximum and Minimum on an Interval

If a <= x <= b and 0 in [a,b], then 0 <= |x| <= max(|a|,|b|).

Working rule on closed interval: compute f'(x), find critical points, evaluate f at critical points and end-points, then compare values.

3. Local Maxima, Local Minima, and Critical Points

f(c) >= f(x) for all x in (c-h, c+h), h>0

f(c) <= f(x) for all x in (c-h, c+h), h>0

f'(x)=0

4. First Derivative Test

If f'(x)>0 just left of c and f'(x)<0 just right of c, then local maximum at x=c.

If f'(x) keeps the same sign on both sides of c, then neither local maximum nor local minimum; c is a point of inflexion.

Critical Points, Stationary Points, and Inflexion

Stationary points or turning points are the values of x for which f'(x) = 0.

Second Derivative Test

If f'(c) = 0 and f''(c) < 0, then f has a local maximum at c.

If f'(c) = 0 and f''(c) = 0, no conclusion comes from the second derivative test.

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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 formulas are in Applications Of Derivatives - II?
This sheet lists 10 formulas from Applications Of Derivatives - II, 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 - II for the ICSE Class 12 board exam?
Learn the core ideas first, then work through the 52 practice questions on Applications Of Derivatives - II. 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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