Q.1 (C) (iii) If f(x)=x·log x then its minimum value is _____.

Answer: -1/e f'(x)=log x+1=0⇒ log x=-1⇒ x=1/e . f''(x)=1/xgt 0 at x=1/e , so f is minimum there. Minimum value =1/elog1/e=-1/e .

If \(f(x)=x\cdot\log x\) then its minimum value is _____.

Q.1 (C) (iii) If \(f(x)=x\cdot\log x\) then its minimum value is _____.

Doubtly Asked 28 Oct 2026 Board exam · March 2026 hsc 12th Save WhatsApp Report

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Answer: \(-\frac{1}{e}\)

\(f'(x)=\log x+1=0\Rightarrow \log x=-1\Rightarrow x=\frac{1}{e}\). \(f''(x)=\frac{1}{x}\gt 0\) at \(x=\frac{1}{e}\), so f is minimum there. Minimum value \(=\frac{1}{e}\log\frac{1}{e}=-\frac{1}{e}\).

Doubtly AI · 28 Oct 2026 AI-verified · Oct 2026 Report

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If \(f(x)=x\cdot\log x\) then its minimum value is _____.

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