Verified Solution • 2025–26 Session moderate

QJEEM24Mab74e: JEE Main 2024 Mathematics - Class 12 JEEM24Mab74e Solution: Let f ( x ) = ( x + 3 ) 2 ( x − 2 ) 3 , x ∈ [ − 4 , 4 ] . If M…

Let f(x)=(x+3)2(x−2)3,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

Multiple Choice Options

  • A 108
  • B 392
  • C 608
  • D 600

Step-by-Step Verified Solution

f′(x)=(x+3)2⋅3(x−2)2+(x−2)32(x+3)=5(x+3)(x−2)2(x+1)f′(x)=0,x=−3,−1,2

JEE Main 2024 (Online) 30th January Evening Shift Mathematics - Application of Derivatives Question 22 English Explanation

f(−4)=−216f(−3)=0,f(4)=49×8=392M=392,m=−216M−m=392+216=608 Ans = '3' 

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