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