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MHT CET202019 Oct 2020Morning ShiftMathematicsApplication of DerivativesActual

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

Options

  1. Adecreasing in (- ,-1) and increasing in (-1, )
  2. Bdecreasing for all x
  3. Cincreasing in (- ,-1) and decreasing in (-1, )
  4. Dincreasing for all x

Correct answer

C. increasing in (- ,-1) and decreasing in (-1, )

Step-by-step solution

(C) Given array l f(x)=(x+2) e^ -x aligned f^ (x) &=(x+2) (e^ -x )(-1)+e^ -x (1) &=e^ -x [1-(x+2)]=e^ -x (-x-1) &=-e^ -x (x+1) aligned array Here e^ -x is always positive. array l Now -(x+1)>0 -x>1 x -1 array Thus f ( x ) increases in (- ,-1) and decreases in (-1, )

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