Function Expression :
\[f(x)=\sqrt{x^2-x} \]Domain
\[\left]-\infty, 0\right] \cup \left[1, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = +\infty \]\[\lim_{x \overset{<}{\rightarrow0} }f(x) = 0 \]
\[\lim_{x \overset{>}{\rightarrow1} }f(x) = 0 \]
\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{x - \frac{1}{2}}{\sqrt{x^{2} - x}} \]\[f^{\,\prime}(x)=\frac{x - \frac{1}{2}}{\sqrt{x \left(x - 1\right)}} \]
\[f^{\,\prime}(x)=\frac{2 x - 1}{2 \sqrt{x \left(x - 1\right)}} \]
Integral
\[F(x) = \int \sqrt{x^{2} - x}\, dx \]Sign Table
Variation Table
Plot
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