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Saturday, 31 October

JEE Main · Maths · Continuity and Differentiability

Differentiability of Max/Min Functions

JEE Main asked Differentiability of Max/Min Functions 6 times in 6 of the 108 shifts Lumi analysed, in 2020, 2021, 2022, 2023 and 2026. It belongs to Continuity and Differentiability (Maths). The longest wait between two years asking it was 3 years. In 2021 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
6
in 6 shifts
Years
5 of 8
First asked
2020
last in 2026
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020, 2021, 2022, 2023 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.10.20’170.08’200.07’210.04’220.07’230’240’250.11’26

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 2 in 24 shifts · 2022: 1 in 24 shifts · 2023: 1 in 12 shifts · 2024: 0 in 18 shifts · 2025: 0 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
  • 20250 of 8
  • 20240 of 18
  • 20231 of 12
  • 20221 of 24
  • 20212 of 24
  • 20201 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: application.

  • Count non-differentiable points of composite function
  • Non-differentiable points of max of two functions

Difficulty

Easy 1Medium 2Hard 3

2 of the 6 questions had a numerical answer.

Every question

All 6 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 1 · Q25The number of points, at which the function f(x)=max⁡{6x, 2+3x2}+∣x−1∣cos⁡∣x2−14∣f(x)=\max\{6x,\ 2+3x^2\}+|x-1|\cos\left|x^2-\frac14\right|, x∈(−π,π)x\in(-\pi,\pi), is not…HardNumerical value
  2. 15 Apr 2023, Shift 1 · Q9Let [x][x] denote the greatest integer function and f(x)=max⁡{1+x+[x],2+x,x+2[x]}f(x)=\max\{1+x+[x], 2+x, x+2[x]\}, 0≤x≤20\le x\le 2. Let mm be the number of points in…HardSingle correct
  3. 26 Jun 2022, Shift 2 · Q5Let f(x)=min⁡{1,1+xsin⁡x},0≤x≤2πf(x) = \min\{1, 1 + x \sin x\}, 0 \leq x \leq 2\pi. If mm is the number of points, where ff is not differentiable and nn is the…MediumSingle correct
  4. 25 Feb 2021, Shift 2 · Q81A function ff is defined on [−3,3][-3, 3] as…HardNumerical value
  5. 26 Aug 2021, Shift 2 · Q76Let [t][t] denote the greatest integer less than or equal to t. Let f(x)=x−[x]f(x)=x-[x], g(x)=1−x+[x]g(x)=1-x+[x], and h(x)=min⁡{f(x),g(x)}h(x)=\min\{f(x),g(x)\},…MediumSingle correct
  6. 6 Sep 2020, Shift 2 · Q58Let f:R→Rf:\mathbf{R}\to\mathbf{R} be a function defined by f(x)=max⁡{x,x2}f(x)=\max\{x,x^2\}. Let S denote the set of all points in R\mathbf{R}, where…EasySingle correct

Shifts: 6 Sep 2020, Shift 2, 25 Feb 2021, Shift 2, 26 Aug 2021, Shift 2, 26 Jun 2022, Shift 2, 15 Apr 2023, Shift 1, 4 Apr 2026, Shift 1.

Same topic

Other ideas in Continuity and Differentiability

Continuity and Differentiability has 18 ideas JEE Main has asked; 13 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas