Function Expression :
\[f(x)=\frac{3x^2-4x}{(x-1 )^2} \]Domain
\[\left]-\infty, 1\right[ \cup \left]1, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = 3 \]\[\lim_{x \overset{<}{\rightarrow1} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow1} }f(x) = -\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = 3 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{\left(2 - 2 x\right) \left(3 x^{2} - 4 x\right)}{\left(x - 1\right)^{4}} + \frac{6 x - 4}{\left(x - 1\right)^{2}} \]\[f^{\,\prime}(x)=\frac{2 \cdot \left(2 - x\right)}{x^{3} - 3 x^{2} + 3 x - 1} \]
\[ \]
Integral
\[F(x) = 3 x + 2 \log{\left(x - 1 \right)} + \frac{1}{x - 1} \]Sign Table
Variation Table
Plot
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