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Formula
Solve the cubic equation
Answer
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Graph
$y = x ^ { 3 } - 8$
$y = 0$
$x$Intercept
$\left ( 2 , 0 \right )$
$y$Intercept
$\left ( 0 , - 8 \right )$
Derivative
$3 x ^ { 2 }$
Seconde derivative
$6 x$
Local Maximum
$\left ( 0 , - 8 \right )$
Point of inflection
$\left ( 0 , - 8 \right )$
$x ^{ 3 } -8 = 0$
$x = 2$
Solve the cubic equation
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 8 } = \color{#FF6800}{ 0 }$
$ $ Organize the expression $ $
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } = \color{#FF6800}{ 0 } \color{#FF6800}{ + } \color{#FF6800}{ 8 }$
$x ^ { 3 } = \color{#FF6800}{ 0 } + 8$
$ $ 0 does not change when you add or subtract $ $
$x ^ { 3 } = 8$
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } = \color{#FF6800}{ 8 }$
$ $ Do the cube root on both sides of the equation $ $
$\color{#FF6800}{ x } = \sqrt[ \color{#FF6800}{ 3 } ]{ \color{#FF6800}{ 8 } }$
$x = \sqrt[ \color{#FF6800}{ 3 } ]{ \color{#FF6800}{ 8 } }$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$x = \color{#FF6800}{ 2 }$
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