JEE Main 2024MathematicsApplication of DerivativesEasyMCQ

JEE Main 2024 — Application of Derivatives Question with Solution

JEE Main 2024 (30 Jan Shift 2)

Question

Let fx=x+32x-23,x∈[-4,4]. If M and m are the maximum and minimum values of f, respectively in [-4,4], then the value of M-m is :

Choose an option

Show full solutionCorrect option: C
Correct answer
C608

Step-by-step explanation

Given: fx=x+32x-23

⇒f'x=x+32×3x-22+x-232x+3

⇒f'x=x+3x-22x+3×3+x-22

⇒f'x=x+3x-223x+9+2x-4

⇒f'x=x+3x-225x+5

⇒f'x=5x+3x-22x+1

For critical points, we put f'x=0.

⇒5x+3x-22x+1=0

⇒x=-3, 2, -1

⇒f-3=f2=0

⇒f-1=22-33=-108

Also, x∈-4,4

⇒f(-4)=-216

⇒f(4)=49×8=392

⇒M=392, m=-216

⇒M-m=392+216

⇒M-m=608

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About this question

This is a previous-year question from JEE Main 2024, covering the Application of Derivatives 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.