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Solve the following
Answer
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Graph
$y = x ^ { 3 } + 2 x ^ { 2 } + 3 x + 3$
$y = 0$
$x$Intercept
$\left ( - \dfrac { \sqrt[ 3 ]{ \dfrac { 43 } { 2 } + \dfrac { 9 \sqrt{ 29 } } { 2 } } } { 3 } - \dfrac { 2 } { 3 } + \dfrac { 5 } { 3 \left ( \dfrac { 43 } { 2 } + \dfrac { 9 \sqrt{ 29 } } { 2 } \right ) ^ { \frac { 1 } { 3 } } } , 0 \right )$
$y$Intercept
$\left ( 0 , 3 \right )$
Derivative
$3 x ^ { 2 } + 4 x + 3$
Seconde derivative
$6 x + 4$
Point of inflection
$\left ( - \dfrac { 2 } { 3 } , \dfrac { 43 } { 27 } \right )$
$\dfrac { - 40 \sqrt[ 3 ]{ 2 } + \left ( - 8 + \sqrt[ 3 ]{ 4 } \left ( 1 + \sqrt{ 3 } i \right ) \sqrt[ 3 ]{ 43 + 9 \sqrt{ 29 } } \right ) \left ( 1 + \sqrt{ 3 } i \right ) \sqrt[ 3 ]{ 43 + 9 \sqrt{ 29 } } } { 12 \left ( 1 + \sqrt{ 3 } i \right ) \left ( 43 + 9 \sqrt{ 29 } \right ) ^ { \frac { 1 } { 3 } } }$
Calculate the value
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