Function Expression :
\[f(x)=-\frac{3}{2}x^2+\frac{1}{2}x^2ln(x )-x \]Domain
\[\left]0, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = 0 \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=x \log{\left(x \right)} - \frac{5 x}{2} - 1 \]\[f^{\,\prime}(x)=x \log{\left(x \right)} - \frac{5 x}{2} - 1 \]
\[f^{\,\prime}(x)=\frac{2 x \log{\left(x \right)} - 5 x - 2}{2} \]
Integral
\[F(x) = \frac{x^{3} \log{\left(x \right)}}{6} - \frac{5 x^{3}}{9} - \frac{x^{2}}{2} \]Sign Table
Variation Table
Plot
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