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Formula
Graph
$y = x ^ { 4 } - 6 x ^ { 3 } + 10 x ^ { 2 } - 6 x + 1$
$y = 0$
$x$Intercept
$\left ( \sqrt{ 3 } + 2 , 0 \right )$, $\left ( 1 , 0 \right )$, $\left ( 2 - \sqrt{ 3 } , 0 \right )$
$y$Intercept
$\left ( 0 , 1 \right )$
Derivative
$4 x ^ { 3 } - 18 x ^ { 2 } + 20 x - 6$
Seconde derivative
$12 x ^ { 2 } - 36 x + 20$
Local Minimum
$\left ( \dfrac { 1 } { 2 } , - \dfrac { 3 } { 16 } \right )$, $\left ( 3 , - 8 \right )$
Local Maximum
$\left ( 1 , 0 \right )$
Point of inflection
$\left ( \dfrac { 3 } { 2 } - \dfrac { \sqrt{ 21 } } { 6 } , - 8 - 6 \left ( \dfrac { 3 } { 2 } - \dfrac { \sqrt{ 21 } } { 6 } \right ) ^ { 3 } + \left ( \dfrac { 3 } { 2 } - \dfrac { \sqrt{ 21 } } { 6 } \right ) ^ { 4 } + \sqrt{ 21 } + 10 \left ( \dfrac { 3 } { 2 } - \dfrac { \sqrt{ 21 } } { 6 } \right ) ^ { 2 } \right )$, $\left ( \dfrac { \sqrt{ 21 } } { 6 } + \dfrac { 3 } { 2 } , - 6 \left ( \dfrac { \sqrt{ 21 } } { 6 } + \dfrac { 3 } { 2 } \right ) ^ { 3 } - 8 - \sqrt{ 21 } + \left ( \dfrac { \sqrt{ 21 } } { 6 } + \dfrac { 3 } { 2 } \right ) ^ { 4 } + 10 \left ( \dfrac { \sqrt{ 21 } } { 6 } + \dfrac { 3 } { 2 } \right ) ^ { 2 } \right )$
$x ^{ 4 } -6x ^{ 3 } +10x ^{ 2 } -6x+1 = 0$
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