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Saturday, 31 October

JEE Main · Maths · Application of Derivatives

Second Derivative Test

JEE Main asked Second Derivative Test 3 times in 3 of the 108 shifts Lumi analysed, all in 2021. It belongs to Maxima and Minima, in Application of Derivatives (Maths). In 2021 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
3
in 3 shifts
Years
1 of 8
First asked
2021
the only year
Pattern
Gone quiet
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2021. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.050.10’170’200.10’210’220’230’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 3 in 24 shifts · 2022: 0 in 24 shifts · 2023: 0 in 12 shifts · 2024: 0 in 18 shifts · 2025: 0 in 8 shifts · 2026: 0 in 9 shifts.

Shift by shift

Each square is one analysed shift, in date order. Open a filled one for that paper.

  • 20260 of 9
  • 20250 of 8
  • 20240 of 18
  • 20230 of 12
  • 20220 of 24
  • 20213 of 24
  • 20200 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Numerical value is the usual form. Skill tested: multi-step.

  • Minimum value of function from derivative condition
  • Local minimum of rational function

Difficulty

Easy 1Medium 2Hard 0

2 of the 3 questions had a numerical answer.

Every question

All 3 questions

From the official JEE Main shift papers, newest first. Open one for the full question, the options and the official answer.

  1. 26 Feb 2021, Shift 1 · Q68The maximum slope of the curve y=12x4−5x3+18x2−19xy=\frac{1}{2}x^4-5x^3+18x^2-19x occurs at the point :MediumSingle correct
  2. 4 Aug 2021, Shift 2 · Q87If ff be a twice differentiable function satisfying f(x)=x4+x2f′′(1)+f′′(2)f(x)=x^4+x^2f''(1)+f''(2), then the modulus of the minimum value of f(x)f(x) is equal…MediumNumerical value
  3. 4 Aug 2021, Shift 1 · Q85The local minimum value of (5+x)(2+x)(1+x)\frac{(5+x)(2+x)}{(1+x)}, (x≠−1)(x\neq-1), is ________.EasyNumerical value

Shifts: 26 Feb 2021, Shift 1, 4 Aug 2021, Shift 2, 4 Aug 2021, Shift 1.

Same topic

Other ideas in Maxima and Minima

Maxima and Minima has 31 ideas JEE Main has asked; 14 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas