JEE Main20244 Apr 2024Evening ShiftMathematicsApplication of DerivativesActual

Let f(x)=3 x-2 + 4-x be a real valued function. If and are respectively the minimum and the maximum values of f , then ^2+2 ^2 is equal to

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Correct answer

A. 42

Step-by-step solution

aligned & f(x)=3 x-2 + 4-x & x-2 0 & 4-x 0 & x [2,4] aligned Let x=2 ^2 +4 ^2 aligned & f ( x )=3 2 | |+ 2 | | & 2 3 2 | |+ 2 | | 9 2+2 & 2 3 2 | |+ 2 | | 20 & = 2 = 20 & ^2+2 ^2=2+40=42 aligned

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