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Solve the following

Answer

Graph

$y = \left ( x + 1 \right ) \left ( x + 3 \right ) \left ( x + 5 \right ) \left ( x + 7 \right )$

$y = - 15$

$x$Intercept

$\left ( - 5 , 0 \right )$, $\left ( - 7 , 0 \right )$, $\left ( - 1 , 0 \right )$, $\left ( - 3 , 0 \right )$

$y$Intercept

$\left ( 0 , 105 \right )$

Derivative

$4 x ^ { 3 } + 48 x ^ { 2 } + 172 x + 176$

Seconde derivative

$12 x ^ { 2 } + 96 x + 172$

Local Minimum

$\left ( - 4 - \sqrt{ 5 } , 16 \left ( - 4 - \sqrt{ 5 } \right ) ^ { 3 } - 599 - 176 \sqrt{ 5 } + \left ( - 4 - \sqrt{ 5 } \right ) ^ { 4 } + 86 \left ( - 4 - \sqrt{ 5 } \right ) ^ { 2 } \right )$, $\left ( - 4 + \sqrt{ 5 } , - 599 + 16 \left ( - 4 + \sqrt{ 5 } \right ) ^ { 3 } + \left ( - 4 + \sqrt{ 5 } \right ) ^ { 4 } + 86 \left ( - 4 + \sqrt{ 5 } \right ) ^ { 2 } + 176 \sqrt{ 5 } \right )$

Local Maximum

$\left ( - 4 , 9 \right )$

Point of inflection

$\left ( - 4 - \dfrac { \sqrt{ 15 } } { 3 } , 16 \left ( - 4 - \dfrac { \sqrt{ 15 } } { 3 } \right ) ^ { 3 } - 599 - \dfrac { 176 \sqrt{ 15 } } { 3 } + \left ( - 4 - \dfrac { \sqrt{ 15 } } { 3 } \right ) ^ { 4 } + 86 \left ( - 4 - \dfrac { \sqrt{ 15 } } { 3 } \right ) ^ { 2 } \right )$, $\left ( - 4 + \dfrac { \sqrt{ 15 } } { 3 } , - 599 + 16 \left ( - 4 + \dfrac { \sqrt{ 15 } } { 3 } \right ) ^ { 3 } + \left ( - 4 + \dfrac { \sqrt{ 15 } } { 3 } \right ) ^ { 4 } + \dfrac { 176 \sqrt{ 15 } } { 3 } + 86 \left ( - 4 + \dfrac { \sqrt{ 15 } } { 3 } \right ) ^ { 2 } \right )$

$- 6$

Calculate the value

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