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MHT CET20244 May 2024Morning ShiftMathematicsApplication of DerivativesActual

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

Options

  1. Aincreasing on (0, ) .
  2. Bincreasing on (0, e ) , decreasing on ( e , ) .
  3. Cdecreasing on (0, ) .
  4. Ddecreasing on (0, e ) , increasing on ( e , )

Correct answer

C. decreasing on (0, ) .

Step-by-step solution

aligned & Let f (x)= ( +x) ( e +x) & aligned f ^ (x) & = ( e +x) 1 +x - ( +x) 1 e +x [ ( e +x)]^2 & = ( e +x) ( e +x)-( +x) ( +x) [ ( e +x)]^2 ( e +x)( +x) f^ (x) & 0 for all x 0 f (x) & is decreasing on (0, ) . aligned aligned

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