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Formula
Graph
$y = x ^ { 3 } + 6 x ^ { 2 } + 6 x + 5$
$y = 0$
$x$Intercept
$\left ( - 5 , 0 \right )$
$y$Intercept
$\left ( 0 , 5 \right )$
Derivative
$3 x ^ { 2 } + 12 x + 6$
Seconde derivative
$6 x + 12$
Local Minimum
$\left ( - 2 + \sqrt{ 2 } , - 7 + \left ( - 2 + \sqrt{ 2 } \right ) ^ { 3 } + 6 \left ( - 2 + \sqrt{ 2 } \right ) ^ { 2 } + 6 \sqrt{ 2 } \right )$
Local Maximum
$\left ( - 2 - \sqrt{ 2 } , \left ( - 2 - \sqrt{ 2 } \right ) ^ { 3 } - 6 \sqrt{ 2 } - 7 + 6 \left ( - 2 - \sqrt{ 2 } \right ) ^ { 2 } \right )$
Point of inflection
$\left ( - 2 , 9 \right )$
$x ^{ 3 } +6x ^{ 2 } +6x+5 = 0$
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