Function Expression :
\[f(x)=\frac{-x^2+5x-9}{x-5} \]Domain
\[\left]-\infty, 5\right[ \cup \left]5, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = +\infty \]\[\lim_{x \overset{<}{\rightarrow5} }f(x) = +\infty \]
\[\lim_{x \overset{>}{\rightarrow5} }f(x) = -\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = -\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{5 - 2 x}{x - 5} - \frac{- x^{2} + 5 x - 9}{\left(x - 5\right)^{2}} \]\[f^{\,\prime}(x)=\frac{- x^{2} + 10 x - 16}{x^{2} - 10 x + 25} \]
\[ \]
Integral
\[F(x) = - \frac{x^{2}}{2} - 9 \log{\left(x - 5 \right)} \]Sign Table
Variation Table
Plot
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