Function Expression :
\[f(x)=-2e^{-x+1}+4x^2+2x-1 \]Domain
\[]-\infty ;+\infty [ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = -\infty \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=8 x + 2 e^{1 - x} + 2 \]\[f^{\,\prime}(x)=8 x + 2 e^{1 - x} + 2 \]
\[f^{\,\prime}(x)=2 \cdot \left(4 x + e^{1 - x} + 1\right) \]
Integral
\[F(x) = \frac{4 x^{3}}{3} + x^{2} - x + 2 e^{1 - x} \]Sign Table
Variation Table
Plot
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