JEE Main 2023MathematicsContinuity and DifferentiabilityMediumMCQ

JEE Main 2023 — Continuity and Differentiability Question with Solution

JEE Main 2023 (15 Apr Shift 1)

Question

Let x denote the greatest integer function and fx=max1+x+x, 2+x, x+2x, 0≤x≤2, where f is not continuous and n be the number of points in 0, 2, where f is not differentiable. Then m+n2+2 is equal to 

Choose an option

Show full solutionCorrect option: D
Correct answer
D3

Step-by-step explanation

Given,

fx=max1+x+x, 2+x, x+2x, 0≤x≤2

⇒fx=maxx+1, x+2, x0≤x<1maxx+2, x+2, x+21≤x<2max5, 4, 6x=2

⇒fx=x+2,0≤x<1x+2,1≤x<26,x=2

⇒f(x)=x+20≤x<26x=2

So, f is not continuous at x=2 as f2-=4 & f2=6

And f is differentiable in 0, 2 as x+2 is a linear function,

∴ m=1, n=0

⇒m+n2+2=1+2=3

Hence this is the required option.

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About this question

This is a previous-year question from JEE Main 2023, covering the Continuity and Differentiability chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.