Skip to main content
Super TutorResources
Chapter 13 of 13
Chapter Summary

Applications Of Derivatives - II — Chapter Summary

ICSE · Class 12 · Mathematics

Summary of Applications Of Derivatives - II for ICSE Class 12 Mathematics. Part of the ICSE Class 12 Mathematics syllabus.

52 questions29 flashcards10 formulas & key relations5 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 chapter summary and more.

Try Super Tutor — Free

Free trial, no card needed.

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

One of 4 illustrations for Applications Of Derivatives - II in Super Tutor — alongside flashcards, concept maps and practice questions.

Overview

Maxima, minima, and optimisation form the core of this chapter. A function may reach a highest or lowest value over its whole domain, or only near a point. The first idea is absolute extremum over an entire interval or domain, and the second is local extremum within a neighbourhood. The chapter also

Key Concepts

Absolute maximum is the greatest value

Absolute maximum is the greatest value of a function on an interval, while absolute minimum is the least value on that interval. Both are defined over

A local maximum is greater than

A local maximum is greater than or equal to nearby function values, and a local minimum is less than or equal to nearby values. These are neighbourhoo

Stationary points are values where f'(x)=0

Stationary points are values where f'(x)=0. Critical points are values where either f'(x)=0 or f'(x) does not exist. Every stationary point is a criti

If f'(x) changes from positive

If f'(x) changes from positive to negative at c, then f has a local maximum at c. If f'(x) changes from negative to positive, then f has a local minim

If f'(c)=0 and f''(c)<0

If f'(c)=0 and f''(c)<0, then f has a local maximum at c. If f'(c)=0 and f''(c)>0, then f has a local minimum at c. If f''(c)=0, the test gives no con

Learning Objectives

  • Distinguish between absolute and local maxima and minima
  • Identify stationary points and critical points correctly
  • Use the first derivative test to classify local extrema and inflexion points
  • Use the second derivative test to classify local maxima and minima
  • Find absolute extrema on closed intervals using derivatives

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 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.

More resources for Applications Of Derivatives - II

All ICSE Class 12 Mathematics Chapter Summary

For serious students

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

Quizzes, flashcards, an AI doubt solver and a study plan for ICSE Class 12 Mathematics. Free to start, no card needed.

Try Super Tutor Free
Try this chapter free