Function Expression :
\[f(x)=\frac{2}{(x-3 )^3} \]Domain
\[\left]-\infty, 3\right[ \cup \left]3, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = 0 \]\[\lim_{x \overset{<}{\rightarrow3} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow3} }f(x) = +\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = 0 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- \frac{6}{\left(x - 3\right)^{4}} \]\[f^{\,\prime}(x)=- \frac{6}{\left(x - 3\right)^{4}} \]
\[ \]
Integral
\[F(x) = - \frac{2}{2 x^{2} - 12 x + 18} \]Sign Table
Variation Table
Plot
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