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MHT CET202416 May 2024Morning ShiftMathematicsApplication of DerivativesActual

The set of all points, for which f (x)=x^2 e ^ - x strictly increases, is

Options

  1. A(0,2)
  2. B(2, )
  3. C(-2,0)
  4. D(- , )

Correct answer

A. (0,2)

Step-by-step solution

f ^ (x)=2 x e ^ -x -x^2 e ^ -x =x e ^ -x (2-x) Since f is increasing, f ^ (x) 0 aligned & x e ^ -x (2-x) 0 & x(2-x) 0 & 0 x 2 & x (0,2) aligned

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