Skip to main content
Super TutorResources
Chapter 13 of 13
QuestionsNotesFlashcardsSummaryFormulasQuizConceptsSyllabusPlan
Flashcards

Applications Of Derivatives - II

ICSE · Class 12 · Mathematics

Flashcards for Applications Of Derivatives - II — ICSE Class 12 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.

52 questions29 flashcards5 concepts

Interactive on Super Tutor

Studying Applications Of Derivatives - II? Get the full interactive chapter.

Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for flashcards and more.

Try Super Tutor — Free

1,000+ Class 12 students started this chapter today

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.
Super Tutor

Learn better with visuals Super Tutor has hundreds of illustrations like this across every chapter — all free to try.

Get started
29 Flashcards
Card 1Absolute extrema on the real line

Solve for the absolute maximum and absolute minimum of f(x)=|x| on R.

Answer

Step 1: For every real x, |x| >= 0. Step 2: The smallest value is 0, and it occurs at x = 0. Step 3: There is no largest value because |x| keeps growing as |x| becomes larger. Answer: Absolute minimum…

Card 2Absolute extrema on a closed interval

Find the absolute maximum and absolute minimum of f(x)=|x| on [2,5].

Answer

Step 1: On [2,5], x is positive, so |x| = x. Step 2: The smallest value on the interval is at x = 2. Step 3: The largest value on the interval is at x = 5. Step 4: f(2)=2 and f(5)=5. Answer: Absolute …

Card 3Local extrema and end points

Why can a local maximum or local minimum not occur at an end point of an interval?

Answer

A local extremum needs a whole neighbourhood around the point. At an end point, there is no open interval on both sides inside the domain, so the neighbourhood condition fails. Example: an end point c…

Card 4Critical points

Find the critical points of f(x)=x^3+x^2+x+1.

Answer

Step 1: Differentiate: f'(x)=3x^2+2x+1. Step 2: Set f'(x)=0: 3x^2+2x+1=0. Step 3: The discriminant is 2^2-4(3)(1)=4-12=-8, so there are no real roots. Step 4: f'(x) does not fail to exist anywhere. An…

Card 5First derivative test

Solve: Find the local maximum or minimum of f(x)=2x^3-6x^2+6x+5 using the first derivative test.

Answer

Step 1: Differentiate: f'(x)=6x^2-12x+6=6(x-1)^2. Step 2: Critical point: f'(x)=0 gives x=1. Step 3: Check sign near x=1. Since 6(x-1)^2 is positive on both sides of 1, the sign does not change. Step …

Card 6First derivative test

Find the local maximum and local minimum of f(x)=(x-3)^4 using the first derivative test.

Answer

Step 1: f'(x)=4(x-3)^3. Step 2: Set f'(x)=0 gives x=3. Step 3: For x slightly less than 3, f'(x)<0. For x slightly more than 3, f'(x)>0. Step 4: Negative to positive means local minimum. Step 5: f(3)=…

Card 7First derivative test

Find the local maximum of f(x)=x*sqrt(1-x) on (0,1).

Answer

Step 1: Differentiate. f'(x)=x*(-1/(2sqrt(1-x)))+sqrt(1-x)=(2-3x)/(2sqrt(1-x)). Step 2: Set numerator equal to zero: 2-3x=0, so x=2/3. Step 3: For x slightly less than 2/3, f'(x)>0. Step 4: For x slig…

Card 8Second derivative test

Use the second derivative test for f(x)=2x^3-21x^2+36x-20.

Answer

Step 1: f'(x)=6x^2-42x+36=6(x-1)(x-6). Step 2: Critical points are x=1 and x=6. Step 3: f''(x)=12x-42. Step 4: f''(1)= -30 < 0, so x=1 is a local maximum. Step 5: f(1)=2-21+36-20=-3. Step 6: f''(6)=30…

+21 more flashcards available

Practice All

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.
How many flashcards are available for Applications Of Derivatives - II?
There are 29 flashcards for Applications Of Derivatives - II covering key definitions, formulas, and concepts. Use them daily for 10–15 minutes for best results.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

More resources for Applications Of Derivatives - II

All 13 chapters — ICSE Class 12 Mathematics Flashcards

For serious students

Get the full Applications Of Derivatives - II chapter — for free.

Quizzes, flashcards, AI doubt-solver and a step-by-step study plan for ICSE Class 12 Mathematics.

Try Super Tutor Free
Try the full chapter — Free