JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 26 July 2022, Shift 1, Maths Q9

Question 9 of 90 in this shift, Maths question 9 of 30, Section A.

Let

f(x) = \begin{cases} x^3 - x^2 + 10x - 7, & x \leq 1 \\ -2x + \log_2 (\mathrm{b}^2 - 4), & x > 1 \end{cases}

. Then the set of all values of b, for which

f(x)

has maximum value at

x = 1

, is :

(1) $(-6,\ -2)$
(2) $(2,\ 6)$
(3) $[-6,\ -2) \cup (2,\ 6]$ Official answer
(4) $\left[-\sqrt{6},\ -2\right) \cup \left(2,\ \sqrt{6}\right]$

Official answer

Option 3

NTA final key.

Chapter: Application of Derivatives
Topic: Maxima and Minima
Idea tested: Extrema at Piecewise Junctions

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Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.