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Saturday, 31 October

JEE Main · Maths · Application of Derivatives

Critical vs Stationary Points

JEE Main asked Critical vs Stationary Points 3 times in 3 of the 108 shifts Lumi analysed, in 2021, 2024 and 2026. It belongs to Maxima and Minima, in Application of Derivatives (Maths). The longest wait between two years asking it was 3 years.

Updated 2026-10-24

Times asked
3
in 3 shifts
Years
3 of 8
First asked
2021
last in 2026
Pattern
Frequent
across the analysed shifts

Questions on this idea a shift, by year

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

00.10.20’170’200.03’210’220’230.05’240’250.11’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 1 in 24 shifts · 2022: 0 in 24 shifts · 2023: 0 in 12 shifts · 2024: 1 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
  • 20241 of 18
  • 20230 of 12
  • 20220 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

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

  • Count critical points of modulus function
  • Parameter range for no critical points

Difficulty

Easy 0Medium 1Hard 2

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. 2 Apr 2026, Shift 1 · Q18The number of critical points of the function f(x)={∣sin⁡xx∣,x≠01,x=0f(x)=\begin{cases}\left|\frac{\sin x}{x}\right|, & x\neq0\\ 1, & x=0\end{cases} in the…HardSingle correct
  2. 9 Apr 2024, Shift 2 · Q25Let the set of all values of pp, for which f(x)=(p2−6p+8)(sin⁡22x−cos⁡22x)+2(2−p)x+7f(x)=(p^2-6p+8)\left(\sin^2 2x-\cos^2 2x\right)+2(2-p)x+7 does not have any critical point,…MediumNumerical value
  3. 25 Feb 2021, Shift 1 · Q87Let f(x)f(x) be a polynomial of degree 6 in xx, in which the coefficient of x6x^6 is unity and it has extrema at x=−1x = -1 and x=1x = 1. If…HardNumerical value

Shifts: 25 Feb 2021, Shift 1, 9 Apr 2024, Shift 2, 2 Apr 2026, 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