JEE Main 2021 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 31 August 2021, Shift 2, Maths Q68

Question 68 of 90 in this shift, Maths question 8 of 30, Section A.

Let

f

be any continuous function on

[0, 2]

and twice differentiable on

(0, 2)

. If

f(0) = 0

f(1) = 1

and

f(2) = 2

, then :

(1) $f'(x) = 0$ for some $x \in [0, 2]$
(2) $f''(x) > 0$ for all $x \in (0, 2)$
(3) $f''(x) = 0$ for some $x \in (0, 2)$ Official answer
(4) $f''(x) = 0$ for all $x \in (0, 2)$

Official answer

Option 3

NTA final key.

Chapter: Application of Derivatives
Topic: Rolle's Theorem
Idea tested: Higher-Order Derivative Roots

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Asked 4× in all

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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.