Function Expression :
\[f(x)=-x+\frac{3+2ln(x )}{x} \]Domain
\[\left]0, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = -\infty \]\[\lim_{x \rightarrow+\infty}f(x) = -\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=-1 - \frac{2 \log{\left(x \right)} + 3}{x^{2}} + \frac{2}{x^{2}} \]\[f^{\,\prime}(x)=\frac{- x^{2} - 2 \log{\left(x \right)} - 1}{x^{2}} \]
\[ \]
Integral
\[F(x) = - \frac{x^{2}}{2} + \log{\left(x \right)}^{2} + 3 \log{\left(x \right)} \]Sign Table
Variation Table
Plot
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