Function Expression :
\[f(x)=\frac{(x^2-6 )}{2-x} \]Domain
\[\left]-\infty, 2\right[ \cup \left]2, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = +\infty \]\[\lim_{x \overset{<}{\rightarrow2} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow2} }f(x) = +\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = -\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{2 x}{2 - x} + \frac{x^{2} - 6}{\left(2 - x\right)^{2}} \]\[f^{\,\prime}(x)=\frac{x^{2} - 2 x \left(x - 2\right) - 6}{\left(x - 2\right)^{2}} \]
\[ \]
Integral
\[F(x) = - \frac{x^{2}}{2} - 2 x + 2 \log{\left(x - 2 \right)} \]Sign Table
Variation Table
Plot
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