Function Expression :
\[f(x)=\frac{(x^3-4x )}{2x-3} \]Domain
\[\left]-\infty, \frac{3}{2}\right[ \cup \left]\frac{3}{2}, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = +\infty \]\[\lim_{x \overset{<}{\rightarrow\frac{3}{2}} }f(x) = +\infty \]
\[\lim_{x \overset{>}{\rightarrow\frac{3}{2}} }f(x) = -\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{3 x^{2} - 4}{2 x - 3} - \frac{2 \left(x^{3} - 4 x\right)}{\left(2 x - 3\right)^{2}} \]\[f^{\,\prime}(x)=\frac{4 x^{3} - 9 x^{2} + 12}{4 x^{2} - 12 x + 9} \]
\[ \]
Integral
\[F(x) = \frac{x^{3}}{6} + \frac{3 x^{2}}{8} - \frac{7 x}{8} - \frac{21 \log{\left(2 x - 3 \right)}}{16} \]Sign Table
Variation Table
Plot
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