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Formula
Graph
$y = x ^ { 3 } - 6 x ^ { 2 } + 11 x - 6$
$y = 0$
$x$Intercept
$\left ( 3 , 0 \right )$, $\left ( 2 , 0 \right )$, $\left ( 1 , 0 \right )$
$y$Intercept
$\left ( 0 , - 6 \right )$
Derivative
$3 x ^ { 2 } - 12 x + 11$
Seconde derivative
$6 x - 12$
Local Minimum
$\left ( \dfrac { \sqrt{ 3 } } { 3 } + 2 , - 6 \left ( \dfrac { \sqrt{ 3 } } { 3 } + 2 \right ) ^ { 2 } + \dfrac { 11 \sqrt{ 3 } } { 3 } + 16 + \left ( \dfrac { \sqrt{ 3 } } { 3 } + 2 \right ) ^ { 3 } \right )$
Local Maximum
$\left ( 2 - \dfrac { \sqrt{ 3 } } { 3 } , - 6 \left ( 2 - \dfrac { \sqrt{ 3 } } { 3 } \right ) ^ { 2 } - \dfrac { 11 \sqrt{ 3 } } { 3 } + \left ( 2 - \dfrac { \sqrt{ 3 } } { 3 } \right ) ^ { 3 } + 16 \right )$
Point of inflection
$\left ( 2 , 0 \right )$
$x ^{ 3 } -6x ^{ 2 } +11x-6 = 0$
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