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MHT CET20226 Aug 2022Morning ShiftMathematicsApplication of DerivativesActual

The function f(x)= ( +x) (e+x) is

Options

  1. Adecreasing on (0, e ) , increasing on ( e , )
  2. Bincreasing on (0, e ) , decreasing on ( e , )
  3. Cincreasing on (0, )
  4. Ddecreasing on (0, )

Correct answer

D. decreasing on (0, )

Step-by-step solution

aligned & f ( x )= ( + x ) ( e + x ) & f ^ ( x )= 1 + x ( e + x )- ( + x ) 1 e + x ( e + x ) ^2 & f ^ ( x )= ( e + x ) ( e + x )-( + x ) ( + x ) ( + x )( e + x ) ( e + x ) ^2 aligned Let g(x)=(e+x) (e+x)-( +x) ( +x) g ^ ( x )= ( e + x )- ( + x )<0 So, g ( x ) is decreasing aligned & g ( x )< g (0) x (0, ) & ( e + x ) ( e + x )-( + x ) ( + x )< e e - <0 & f ^ ( x )<0 x (0, ) & f ( x ) is decreasing on (0, ) aligned

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