Function Expression :
\[f(x)=\frac{x^3-x^2-13x+4}{x-4} \]Domain
\[\left]-\infty, 4\right[ \cup \left]4, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = +\infty \]\[\lim_{x \overset{<}{\rightarrow4} }f(x) = 27 \]
\[\lim_{x \overset{>}{\rightarrow4} }f(x) = 27 \]
\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{3 x^{2} - 2 x - 13}{x - 4} - \frac{x^{3} - x^{2} - 13 x + 4}{\left(x - 4\right)^{2}} \]\[f^{\,\prime}(x)=2 x + 3 \]
\[ \]
Integral
\[F(x) = \frac{x^{3}}{3} + \frac{3 x^{2}}{2} - x \]Sign Table
Variation Table
Plot
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