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 The set onto which the derivative of the function \mathrm{f(x)=x(\log x-1)} maps the ray \mathrm{[1, \infty)} is

Option: 1

[1, \infty)


Option: 2

(0, \infty)


Option: 3

[0, \infty)


Option: 4

none of these


Answers (1)

best_answer

\mathrm{f^{\prime}(x)=\log x-1+x\left(\frac{1}{x}\right)=\log x}
Since \mathrm{\log x} is an increasing function so \mathrm{f^{\prime}} maps \mathrm{[1, \infty)} onto \mathrm{[0, \infty)}.

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