Function Expression :
\[f(x)=-\frac{x}{2}+\frac{2}{x} \]Domain
\[\left]-\infty, 0\right[ \cup \left]0, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = +\infty \]\[\lim_{x \overset{<}{\rightarrow0} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = +\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = -\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- \frac{1}{2} - \frac{2}{x^{2}} \]\[f^{\,\prime}(x)=\frac{- x^{2} - 4}{2 x^{2}} \]
Integral
\[F(x) = - \frac{x^{2}}{4} + 2 \log{\left(x \right)} \]Sign Table
Variation Table
Plot
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