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NDA 2019 Maths · Mathematics · Application of Derivatives · medium

The local minimum value of f(x)=xln x for x>0 is

Single correct option

The local minimum value of f(x)=xln⁡xf(x)=x\ln x for x>0x>0 is
  1. A. 1e\frac1e
  2. B. −1e-\frac1e
  3. C. 00
  4. D. −e-e
Show answer and solution

Answer: (B) −1e-\frac1e

f′(x)=ln⁡x+1=0f'(x)=\ln x+1=0 gives x=1ex=\frac1e, and f′′(x)=1x>0f''(x)=\frac1x>0, so it is a minimum. The value is f(1e)=1e⋅(−1)=−1ef\left(\frac1e\right)=\frac1e\cdot(-1)=-\frac1e. The value 00 is f(1)f(1), where the derivative is 11, not zero.
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Original question written in the NDA 2019 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