The minimum value of $xlog_ex$ is equal

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Applications of Derivatives

Question:

The minimum value of $xlog_ex$ is equal to

Options:

$\frac{1}{e}$

$-\frac{1}{e}$

$2e$

Correct Answer:

$-\frac{1}{e}$

Explanation:

The correct answer is option (3) → $-\frac{1}{e}$ $\frac{80}{89}$

$y=x\log x$

so $y'=\log x+1=0⇒x=\frac{1}{e}$

$y''=\frac{1}{x}$ so $(y''(\frac{1}{e})=e)>0$

$\frac{1}{e}$ → point of minima

so $y_{min}=y(\frac{1}{e})=-\frac{1}{e}$