Function Expression :
\[f(x)=x(x-1 )(x-2 )(x+6 ) \]Domain
\[]-\infty ;+\infty [ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = +\infty \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=x \left(x - 2\right) \left(x - 1\right) + x \left(x - 2\right) \left(x + 6\right) + x \left(x - 1\right) \left(x + 6\right) + \left(x - 2\right) \left(x - 1\right) \left(x + 6\right) \]\[f^{\,\prime}(x)=4 x^{3} + 9 x^{2} - 32 x + 12 \]
\[ \]
Integral
\[F(x) = \frac{x^{5}}{5} + \frac{3 x^{4}}{4} - \frac{16 x^{3}}{3} + 6 x^{2} \]Sign Table
Variation Table
Plot
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