JEE Main Maths · Application of Derivatives

First Derivative Test

First Derivative Test (Application of Derivatives) was asked 3 times in 3 JEE Main shifts, 2020–2024, out of the 42 shifts Lumi analysed. 1 of the 3 had a numerical answer.

Times asked: 3; in 3 shifts
Years: 2020–2024
Usual format: Single correct; Multi-step
Pattern: Comes in cycles; repeats across shifts

How it is asked

Local minimum location constrained by rational inequality
Find cubic from conditions then local extremum

Difficulty

Easy 0Medium 2Hard 1

Where it sits

Chapter: Application of Derivatives. Topic: Maxima and Minima, 30 questions over 17 ideas.

All 3 questions

Newest first, each with its options and official answer.

9 Apr 2024, Shift 1 · Q27Let the set of all positive values of $\lambda$ , for which the point of local minimum of the function $(1+x(\lambda^2-x^2))$ satisfies…MediumNumerical value
25 Jul 2022, Shift 1 · Q7The curve $y(x)=ax^3+bx^2+cx+5$ touches the $x$ -axis at the point $\mathrm{P}(-2,0)$ and cuts the $y$ -axis at the point $\mathrm{Q}$ ,…MediumSingle correct
6 Sep 2020, Shift 2 · Q60The set of all real values of $\lambda$ for which the function $f(x)=(1-\cos^2 x)\cdot(\lambda+\sin x)$ ,…HardSingle correct