JEE Main 2024MathematicsFunctionsMediumNumerical

JEE Main 2024 — Functions Question with Solution

JEE Main 2024 (29 Jan Shift 1)

Question

Let fx=2x-x2, x∈R. If m and n are respectively the number of points at which the curves y=fx and y=f'x intersects the x-axis, then the value of m+n is

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Show full solutionCorrect answer: 5
Correct answer
5

Step-by-step explanation

Given,

Function fx=2x-x2, x∈R

Now, plotting the diagram of y=2x & y=x2 we get,

Now, from above diagram total point of intersection are three

∴m=3

Now, finding f'(x)=2xln2-2x=0

2xln2=2x

Now, again plotting the diagram of y=2xln2 & y=2x we get,

So, from above diagram total point of intersection is two

∴n=2

Hence, m+n=5

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About this question

This is a previous-year question from JEE Main 2024, covering the Functions 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.