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Solve the following
Answer
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Graph
$y = x ^ { 3 } + 2 x ^ { 2 } - 5 x - 6$
$y = 0$
$x$Intercept
$\left ( 2 , 0 \right )$, $\left ( - 1 , 0 \right )$, $\left ( - 3 , 0 \right )$
$y$Intercept
$\left ( 0 , - 6 \right )$
Derivative
$3 x ^ { 2 } + 4 x - 5$
Seconde derivative
$6 x + 4$
Local Minimum
$\left ( - \dfrac { 2 } { 3 } + \dfrac { \sqrt{ 19 } } { 3 } , - \dfrac { 5 \sqrt{ 19 } } { 3 } - \dfrac { 8 } { 3 } + \left ( - \dfrac { 2 } { 3 } + \dfrac { \sqrt{ 19 } } { 3 } \right ) ^ { 3 } + 2 \left ( - \dfrac { 2 } { 3 } + \dfrac { \sqrt{ 19 } } { 3 } \right ) ^ { 2 } \right )$
Local Maximum
$\left ( - \dfrac { \sqrt{ 19 } } { 3 } - \dfrac { 2 } { 3 } , \left ( - \dfrac { \sqrt{ 19 } } { 3 } - \dfrac { 2 } { 3 } \right ) ^ { 3 } - \dfrac { 8 } { 3 } + \dfrac { 5 \sqrt{ 19 } } { 3 } + 2 \left ( - \dfrac { \sqrt{ 19 } } { 3 } - \dfrac { 2 } { 3 } \right ) ^ { 2 } \right )$
Point of inflection
$\left ( - \dfrac { 2 } { 3 } , - \dfrac { 56 } { 27 } \right )$
$x = - 3 , - 1 , 2 $
Calculate the value
$x ^ { 3 } + 2 x ^ { 2 } - 5 x - 6 = 0$
$ $ Solve $ $ $ $ the $ $ $ $ equation. $ $
$x = - 3 , - 1 , 2 $
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