Function Expression :
\[f(x)=\frac{2-3x}{(x-1 )^2} \]Domain
\[\left]-\infty, 1\right[ \cup \left]1, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = 0 \]\[\lim_{x \overset{<}{\rightarrow1} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow1} }f(x) = -\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = 0 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{\left(2 - 2 x\right) \left(\left(-1\right) 3 x + 2\right)}{\left(x - 1\right)^{4}} - \frac{3}{\left(x - 1\right)^{2}} \]\[f^{\,\prime}(x)=\frac{3 x - 1}{\left(x - 1\right)^{3}} \]
\[ \]
Integral
\[F(x) = - 3 \log{\left(x - 1 \right)} + \frac{1}{x - 1} \]Sign Table
Variation Table
Plot
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