Maxima-Minima - JEE Main Previous Year Question with Solutions

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

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.

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.

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.

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.

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.