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CUET
Maths. Section A
Applications of Derivatives
The function xx decreases on the interval
(0, e)
(0, 1)
$(0, \frac{1}{e})$
None of these
The correct answer is Option 3: $(0, \frac{1}{e})$
⇒ $f'(x) = x^x[1+\log x]$
1+ log$x$ <0
⇒log$x$ < −1
⇒x<1/e
Hence, decreasing on (0, 1/e)