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Formula
Graph
$y = x ^ { 4 } - 7 x ^ { 2 } + 12$
$y = 0$
$x$Intercept
$\left ( 2 , 0 \right )$, $\left ( \sqrt{ 3 } , 0 \right )$, $\left ( - 2 , 0 \right )$, $\left ( - \sqrt{ 3 } , 0 \right )$
$y$Intercept
$\left ( 0 , 12 \right )$
Derivative
$4 x ^ { 3 } - 14 x$
Seconde derivative
$12 x ^ { 2 } - 14$
Local Minimum
$\left ( - \dfrac { \sqrt{ 14 } } { 2 } , - \dfrac { 1 } { 4 } \right )$, $\left ( \dfrac { \sqrt{ 14 } } { 2 } , - \dfrac { 1 } { 4 } \right )$
Local Maximum
$\left ( 0 , 12 \right )$
Point of inflection
$\left ( - \dfrac { \sqrt{ 42 } } { 6 } , \dfrac { 187 } { 36 } \right )$, $\left ( \dfrac { \sqrt{ 42 } } { 6 } , \dfrac { 187 } { 36 } \right )$
$x ^{ 4 } -7x ^{ 2 } +12 = 0$
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