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MHT CET20225 Aug 2022Evening ShiftMathematicsApplication of DerivativesActual

The function f ( x ) is defined by f ( x )=( x +2) e ^ - x is

Options

  1. Amonotonically decreasing in (-1, ) and monotonically increasing in (- ,-1)
  2. Bdecreasing for all x
  3. Cincreasing for all x
  4. Ddecreasing in (- ,-1) and increasing in (-1, )

Correct answer

A. monotonically decreasing in (-1, ) and monotonically increasing in (- ,-1)

Step-by-step solution

aligned & f ( x )=( x +2) e ^ - x f P ^ ( x )= e ^ - x -( x +2) e ^ - x = e ^ - x (1- x -2) & f ^ ( x )=- e ^ - x (1+ x ) sign scheme aligned

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