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AP EAMCET2002MathematicsApplication of Derivatives

The functions f(x)=x e^ -x , (x R) attains a maximum value at x is equal to

Options

  1. A1
  2. B2
  3. C1 e
  4. D3

Correct answer

A. 1

Step-by-step solution

We have, f(x)=x e^ -x f^ (x)=-x e^ -x +e^ -x For maximum or minimum, put f^ (x)=0 aligned & -x e^ -x +e^ -x =0 x=1 & f^ (x)=x e^ -x -e^ -x -e^ -x =(x-2) e^ -x & f^ (1)=(1-2) e⁻¹=- ve aligned f(x) is maximum at x=1 .

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