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NDA 2017 Maths · Mathematics · Application of Derivatives · medium

The maximum value of f(x)=xe^-x for real x is

Single correct option

The maximum value of f(x)=xe−xf(x)=xe^{-x} for real xx is
  1. A. ee
  2. B. 1e\frac1e
  3. C. 1e2\frac1{e^2}
  4. D. 2e\frac2e
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Answer: (B) 1e\frac1e

f′(x)=e−x(1−x)f'(x)=e^{-x}(1-x), so f′=0f'=0 at x=1x=1; f′f' changes from positive to negative there, so it is a maximum with f(1)=1ef(1)=\frac1e. The value 1e2\frac1{e^2} is f(2)f(2) and 2e\frac2e is 2f(1)2f(1).
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Original question written in the NDA 2017 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake