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$y = x ^ { 3 } - 4 x ^ { 2 } + x + 6$

$y = 0$

$x$-intercept

$\left ( 3 , 0 \right )$, $\left ( 2 , 0 \right )$, $\left ( - 1 , 0 \right )$

$y$-intercept

$\left ( 0 , 6 \right )$

Derivative

$3 x ^ { 2 } - 8 x + 1$

Seconde derivative

$6 x - 8$

Local Minimum

$\left ( \dfrac { \sqrt{ 13 } } { 3 } + \dfrac { 4 } { 3 } , - 4 \left ( \dfrac { \sqrt{ 13 } } { 3 } + \dfrac { 4 } { 3 } \right ) ^ { 2 } + \dfrac { \sqrt{ 13 } } { 3 } + \dfrac { 22 } { 3 } + \left ( \dfrac { \sqrt{ 13 } } { 3 } + \dfrac { 4 } { 3 } \right ) ^ { 3 } \right )$

Local Maximum

$\left ( \dfrac { 4 } { 3 } - \dfrac { \sqrt{ 13 } } { 3 } , - \dfrac { \sqrt{ 13 } } { 3 } - 4 \left ( \dfrac { 4 } { 3 } - \dfrac { \sqrt{ 13 } } { 3 } \right ) ^ { 2 } + \left ( \dfrac { 4 } { 3 } - \dfrac { \sqrt{ 13 } } { 3 } \right ) ^ { 3 } + \dfrac { 22 } { 3 } \right )$

Point of inflection

$\left ( \dfrac { 4 } { 3 } , \dfrac { 70 } { 27 } \right )$

$x ^{ 3 } -4x ^{ 2 } +x+6 = 0$

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