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BITSAT2016MathematicsApplication of DerivativesActual

The curve y=x e^ x has minimum value equal to

Options

  1. A- 1 e
  2. B1 e
  3. C- e
  4. De

Correct answer

A. - 1 e

Step-by-step solution

Let y=x e^ x . Differentiate both side w.r.t. 'x'. dy dx = e ^ x + xe ^ x = e ^ x (1+ x ) Put dy dx =0 array l e ^ x (1+ x )=0 x =-1 array Now, d ² y dx ² = e ^ x + e ^ x (1+ x )= e ^ x ( x +2) ( d ² y dx ² )_ ( x =-1) = 1 e +0>0 Hence, y = xe ^ x is minimum function and y _ =- 1 e .

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