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GATE 2014 EE (EE1) – Question 12

Engineering Mathematics · Calculus: Maxima and minima · 1 mark · Multiple choice

Find the maximum of $f(x)=xe^{-x}$ on (0,∞).

  1. $e^{-1}$
  2. $e$
  3. $1-e^{-1}$
  4. $1+e^{-1}$

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Correct answer: (A) $e^{-1}$

Explanation

Differentiate:f′(x)=e⁻ˣ(1−x). This is positive for x<1and negative for x>1, giving the unique maximum at x=1. The requested maximum value is **f(1)=e⁻¹,A**, rather than the location1.