NEW FUNCTION

Function Expression :

\[f(x)=-3x^2. e^{3x} \]

Domain

\[]-\infty ;+\infty [ \]

Limits

\[\lim_{x \rightarrow-\infty}f(x) = 0 \]
\[\lim_{x \rightarrow+\infty}f(x) = -\infty \]
\[ \]

Derivate

\[f^{\,\prime}(x)=- 9 x^{2} e^{3 x} - 6 x e^{3 x} \]
\[f^{\,\prime}(x)=3 x \left(- 3 x - 2\right) e^{3 x} \]
\[ \]

Integral

\[F(x) = \frac{\left(- 9 x^{2} + 6 x - 2\right) e^{3 x}}{9} \]

Sign Table

Variation Table

Plot

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