Class 12 Mathematics — Chapter 6: Application of Derivatives
66 practice questions · 22 Easy · 22 Medium · 22 Hard
Practise Class 12 Mathematics Chapter 6, "Application of Derivatives", with 66 NCERT-aligned multiple-choice questions. The set is split into 22 Easy, 22 Medium and 22 Hard questions, so you can warm up on the fundamentals and then push into the exam-level problems that separate top scorers in CBSE Board exams, JEE Main and JEE Advanced.
"Application of Derivatives" is one of the chapters where problem-solving speed, formula recall and step-by-step reasoning really pays off. Each MCQ on this chapter is timed and uses exam-grade marking (+2 correct, −1 wrong, 0 skipped), training the same accuracy-under-pressure that real papers demand. Every question carries a short explanation, so a wrong answer becomes a quick lesson rather than a dead end — the fastest way to close gaps before a test.
Use this chapter as targeted revision: attempt the Easy set first to confirm your basics on Application of Derivatives, then move to Medium and Hard to test application and problem-solving. Your accuracy, streaks and XP save automatically, and the chapter feeds into your overall Class 12 Mathematics mastery score. A few sample questions are shown below; sign in free to practise all 66.
Key concepts: Application of Derivatives (Class 12 Mathematics)
This chapter applies derivatives to rates of change, increasing/decreasing functions, tangents and normals, and maxima and minima.
- Rate of change
- The derivative dy/dx gives the instantaneous rate of change of y with respect to x; used in related-rates problems.
- Increasing/decreasing
- f is increasing where f'(x) > 0 and decreasing where f'(x) < 0 on an interval.
- Tangent and normal
- The slope of the tangent at a point is f'(x); the normal is perpendicular, with slope −1/f'(x).
- Maxima and minima
- Critical points occur where f'(x) = 0; classify using the first-derivative sign change or the second-derivative test.
- Second-derivative test
- At a critical point, f''(x) > 0 gives a local minimum and f''(x) < 0 gives a local maximum.
Key formulas — Application of Derivatives
💡 Exam tips for Application of Derivatives
- For optimisation (max/min) problems, express the quantity in one variable, differentiate, set f'=0, then verify with f''.
- Always check endpoints too when finding the absolute maximum/minimum on a closed interval.
Sample questions
Rate of change of y w.r.t. x is:
Standard.
If f'(c) = 0 and f''(c) > 0:
Second derivative test.
Maximum area of rectangle inscribed in circle of radius R:
Square diagonal = 2R; area = 2R².
Application of Derivatives — FAQs
What are the key concepts in Class 12 Mathematics Application of Derivatives?+
This chapter applies derivatives to rates of change, increasing/decreasing functions, tangents and normals, and maxima and minima. Key ideas include Rate of change, Increasing/decreasing, Tangent and normal, Maxima and minima, Second-derivative test.
What does Class 12 Mathematics Chapter 6 (Application of Derivatives) cover on XamBaaz?+
It covers 66 NCERT-aligned MCQs on "Application of Derivatives" — 22 Easy, 22 Medium and 22 Hard — each with a timed quiz and an instant explanation, suitable for CBSE Board exams, JEE Main and JEE Advanced.
Are these "Application of Derivatives" questions free to practise?+
Yes — sign in with Google to practise "Application of Derivatives" free. Full unlimited access is ₹999/year (limited-time launch price), with no per-chapter charges.
How should I revise "Application of Derivatives" for the exam?+
Start with the Easy quiz to confirm your fundamentals, then attempt Medium and Hard for application-level practice. Review each explanation, retry the questions you miss, and track your accuracy on this chapter until it is consistently high.
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