Function Expression :
\[f(x)=\sqrt{x^2-3x+2}-x \]Domain
\[\left]-\infty, 1\right] \cup \left[2, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = +\infty \]\[\lim_{x \overset{<}{\rightarrow1} }f(x) = -1 \]
\[\lim_{x \overset{>}{\rightarrow2} }f(x) = -2 \]
\[\lim_{x \rightarrow+\infty}f(x) = - \frac{3}{2} \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{x - \frac{3}{2}}{\sqrt{x^{2} - 3 x + 2}} - 1 \]\[f^{\,\prime}(x)=\frac{x - \sqrt{x^{2} - 3 x + 2} - \frac{3}{2}}{\sqrt{x^{2} - 3 x + 2}} \]
\[f^{\,\prime}(x)=\frac{2 x - 2 \sqrt{x^{2} - 3 x + 2} - 3}{2 \sqrt{x^{2} - 3 x + 2}} \]
Integral
\[F(x) = \int \left(- x + \sqrt{x^{2} - 3 x + 2}\right)\, dx \]Sign Table
Variation Table
Plot
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