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Saturday, 31 October

JEE Main · Maths · Application of Derivatives

Closed Interval Extrema

JEE Main asked Closed Interval Extrema 8 times in 8 of the 108 shifts Lumi analysed, in 2021, 2022, 2023, 2024, 2025 and 2026. It belongs to Maxima and Minima, in Application of Derivatives (Maths). The longest wait between two years asking it was 1 year. In 2022 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
8
in 8 shifts
Years
6 of 8
First asked
2021
last in 2026
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2021, 2022, 2023, 2024, 2025 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.10.20’170’200.03’210.11’220.07’230.05’240.13’250.11’26

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

Shift by shift

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

  • 20261 of 9
  • 20251 of 8
  • 20241 of 18
  • 20231 of 12
  • 20223 of 24
  • 20211 of 24
  • 20200 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Single correct is the usual form. Skill tested: multi-step.

  • Max of trig expression on interval
  • Absolute extrema on interval from critical points

Difficulty

Easy 0Medium 6Hard 2

1 of the 8 questions had a numerical answer.

Every question

All 8 questions

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

  1. 4 Apr 2026, Shift 2 · Q12max⁡0≤x≤π(16sin⁡(x2)cos⁡3(x2))\max_{0\le x\le\pi}\left(16\sin\left(\frac x2\right)\cos^3\left(\frac x2\right)\right) is equal to:MediumSingle correct
  2. 7 Apr 2025, Shift 1 · Q17Let x=−1x = -1 and x=2x = 2 be the critical points of the function f(x)=x3+ax2+blog⁡e∣x∣+1f(x) = x^3 + ax^2 + b\log_e|x| + 1, x≠0x \neq 0. Let mm and MM…MediumSingle correct
  3. 30 Jan 2024, Shift 2 · Q9Let f(x)=(x+3)2(x−2)3f(x) = (x+3)^2 (x-2)^3, x∈[−4,4]x \in [-4, 4]. If MM and mm are the maximum and minimum values of ff, respectively in [−4,4][-4, 4], then…MediumSingle correct
  4. 13 Apr 2023, Shift 1 · Q10max⁡0≤x≤π{x−2sin⁡xcos⁡x+13sin⁡3x}=\max_{0\leq x\leq\pi}\left\{x-2\sin x\cos x+\frac{1}{3}\sin 3x\right\}=HardSingle correct
  5. 24 Jun 2022, Shift 1 · Q12The sum of absolute maximum and absolute minimum values of the function f(x)=∣2x2+3x−2∣+sin⁡xcos⁡xf(x)=|2x^2+3x-2|+\sin x\cos x in the interval [0,1][0, 1] is :HardSingle correct
  6. 28 Jul 2022, Shift 2 · Q67The sum of the absolute maximum and absolute minimum values of the function f(x)=tan⁡−1(sin⁡x−cos⁡x)f(x)=\tan^{-1}(\sin x-\cos x) in the interval [0, π][0,\ \pi] is :MediumSingle correct
  7. 25 Jul 2022, Shift 1 · Q6If the absolute maximum value of the function f(x)=(x2−2x+7) e(4x3−12x2−180x+31)f(x)=(x^2-2x+7)\,\mathrm{e}^{(4x^3-12x^2-180x+31)} in the interval [−3,0][-3,0] is…MediumSingle correct
  8. 17 Mar 2021, Shift 2 · Q85Let f:[−1,1]→Rf:[-1, 1]\to\mathbf{R} be defined as f(x)=ax2+bx+cf(x)=ax^2+bx+c for all x∈[−1,1]x\in[-1, 1], where a,b,c∈Ra, b, c\in\mathbf{R} such that f(−1)=2f(-1)=2,…MediumNumerical value

Shifts: 17 Mar 2021, Shift 2, 24 Jun 2022, Shift 1, 25 Jul 2022, Shift 1, 28 Jul 2022, Shift 2, 13 Apr 2023, Shift 1, 30 Jan 2024, Shift 2, 7 Apr 2025, Shift 1, 4 Apr 2026, Shift 2.

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