JEE Main 2022 · MathsNumerical answerNumerical valueMediumApplication

JEE Main 28 July 2022, Shift 1, Maths Q23

Question 23 of 90 in this shift, Maths question 23 of 30, Section B.

Let

f:[0,1]\to\mathbf{R}

be a twice differentiable function in

(0,1)

such that

f(0)=3

and

f(1)=5

. If the line

y=2x+3

intersects the graph of

f

at only two distinct points in

(0,1)

, then the least number of points

x\in(0,1)

, at which

f''(x)=0

, is __________.

Official answer

NTA final key (2022 Session 2).

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

Same idea in other shifts

Asked 4× in all

4 Apr 2024, Shift 2 · Q25Let $f:\mathbb{R}\to\mathbb{R}$ be a thrice differentiable function such that $f(0)=0, f(1)=1, f(2)=-1, f(3)=2$ and $f(4)=-2$ . Then, the…HardNumerical value
30 Jan 2024, Shift 1 · Q9Let $g:\mathbf{R}\to\mathbf{R}$ be a non constant twice differentiable function such that…HardSingle correct
31 Aug 2021, Shift 2 · Q68Let $f$ 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 :MediumSingle correct

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.