Function Expression :
\[f(x)=\frac{-2x^2+x}{x-1} \]Domain
\[\left]-\infty, 1\right[ \cup \left]1, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = +\infty \]\[\lim_{x \overset{<}{\rightarrow1} }f(x) = +\infty \]
\[\lim_{x \overset{>}{\rightarrow1} }f(x) = -\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = -\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{1 - 4 x}{x - 1} - \frac{\left(-1\right) 2 x^{2} + x}{\left(x - 1\right)^{2}} \]\[f^{\,\prime}(x)=\frac{- 2 x^{2} + 4 x - 1}{x^{2} - 2 x + 1} \]
\[ \]
Integral
\[F(x) = - x^{2} - x - \log{\left(x - 1 \right)} \]Sign Table
Variation Table
Plot
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