Maxima-Minima - JEE Main Previous Year Question with Solutions
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JEE Main Previous Year Question of Math with Solutions are available at eSaral. Practicing JEE Main Previous Year Papers Questions of mathematics will help the JEE aspirants in realizing the question pattern as well as help in analyzing weak & strong areas. eSaral helps the students in clearing and understanding each topic in a better way. eSaral is providing complete chapter-wise notes of Class 11th and 12th both for all subjects. Besides this, eSaral also offers NCERT Solutions, Previous year questions for JEE Main and Advance, Practice questions, Test Series for JEE Main, JEE Advanced and NEET, Important questions of Physics, Chemistry, Math, and Biology and many more. Download eSaral app for free study material and video tutorials. 
Frequently Asked Questions
Find answers to common questions.
Which derivative test is faster for JEE Main — first or second?
The second derivative test is faster for JEE Main because it involves one additional differentiation step rather than sign analysis. Use it first. However, when f″(a) = 0, the second derivative test fails and you must switch to the first derivative test — checking whether f′(x) changes sign around the critical point
What is the difference between local maxima and global maxima in JEE problems?
Local maxima is the highest value of f(x) in a small neighbourhood around a point. Global maxima is the highest value of f(x) over the entire domain or a given interval. JEE Main frequently tests global maxima on closed intervals, which requires evaluating the function at all critical points and both endpoints — not just at f′(x) = 0.
How many questions from Maxima and Minima appear in JEE Main each year?
JEE Main typically includes 1–2 questions from Maxima and Minima every year, each carrying 4 marks. Over the past 6 years (2019–2026), the topic appeared in every single session without exception. Practising PYQs from this topic is one of the most reliable ways to add 4–8 guaranteed marks to your Mathematics score.
How do I know if a critical point is a maximum, minimum, or inflection point?
Apply the second derivative test first: if f″(a) < 0, it is a local maximum; if f″(a) > 0, it is a local minimum. If f″(a) = 0, use the first derivative test: if f′(x) changes from positive to negative through a, it is a local maximum; negative to positive means local minimum; no sign change means inflection point.
What prerequisites do I need before studying Maxima and Minima for JEE Main?
ou need a solid understanding of differentiation rules (chain rule, product rule, quotient rule), behaviour of standard functions (polynomial, trigonometric, exponential, logarithmic), and increasing/decreasing functions. If any of these feel uncertain, revise Chapter 5 and Chapter 6 of Class 12 NCERT — solutions are available at eSaral's NCERT Class 12 Maths Solutions.
Is Maxima and Minima important for JEE Advanced as well?
Yes. JEE Advanced tests Maxima and Minima at a significantly deeper level, including problems involving parametric functions, inequality-based optimisation, and geometry-calculus hybrids. The foundation built through JEE Main PYQs is essential, but additional practice with JEE Advanced PYQs and eSaral's structured problem sets is needed for Advanced.