Function Expression :
\[f(x)=\frac{x^2}{e^x} \]Domain
\[]-\infty ;+\infty [ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = +\infty \]\[\lim_{x \rightarrow+\infty}f(x) = 0 \]
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Derivate
\[f^{\,\prime}(x)=- x^{2} e^{- x} + 2 x e^{- x} \]\[f^{\,\prime}(x)=x \left(2 - x\right) e^{- x} \]
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Integral
\[F(x) = \left(- x^{2} - 2 x - 2\right) e^{- x} \]Sign Table
Variation Table
Plot
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