Function Expression :
\[f(x)=-4xln x \]Domain
\[\left]0, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = 0 \]\[\lim_{x \rightarrow+\infty}f(x) = -\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- 4 \log{\left(x \right)} - 4 \]\[f^{\,\prime}(x)=- 4 \log{\left(x \right)} - 4 \]
\[f^{\,\prime}(x)=4 \left(- \log{\left(x \right)} - 1\right) \]
Integral
\[F(x) = - 2 x^{2} \log{\left(x \right)} + x^{2} \]Sign Table
Variation Table
Plot
Elapsed Time: 0.0166 seconds