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Differentiate
Answer
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Graph
$y = x ^ { 3 } - 2 x - 48$
$x$Intercept
$\left ( \dfrac { 2 } { 3 \left ( \dfrac { 2 \sqrt{ 11658 } } { 9 } + 24 \right ) ^ { \frac { 1 } { 3 } } } + \sqrt[ 3 ]{ \dfrac { 2 \sqrt{ 11658 } } { 9 } + 24 } , 0 \right )$
$y$Intercept
$\left ( 0 , - 48 \right )$
Derivative
$3 x ^ { 2 } - 2$
Seconde derivative
$6 x$
Local Minimum
$\left ( \dfrac { \sqrt{ 6 } } { 3 } , - 48 - \dfrac { 4 \sqrt{ 6 } } { 9 } \right )$
Local Maximum
$\left ( - \dfrac { \sqrt{ 6 } } { 3 } , - 48 + \dfrac { 4 \sqrt{ 6 } } { 9 } \right )$
Point of inflection
$\left ( 0 , - 48 \right )$
$y' = 3x ^ {2} - 2$
Differentiate
$\color{#FF6800}{y} = \color{#FF6800}{x ^ {3} - 2x - 48}$
$ $ Find the derivative of this function $ $
$\color{#FF6800}{y'} = \color{#FF6800}{\dfrac{d}{dx}(x ^ {3} - 2x - 48)}$
$y' = \color{#FF6800}{\dfrac{d}{dx}(x ^ {3} - 2x - 48)}$
$ $ Solve it using $ \dfrac{d}{dx}(f + g) = \dfrac{d}{dx}(f) + \dfrac{d}{dx}(g) $ differentiation $ $
$y' = \color{#FF6800}{\dfrac{d}{dx}(x ^ {3}) + \dfrac{d}{dx}(- 2x) - \dfrac{d}{dx}(48)}$
$y' = \color{#FF6800}{\dfrac{d}{dx}(x ^ {3})} + \dfrac{d}{dx}(- 2x) - \dfrac{d}{dx}(48)$
$ $ Calculate the differentiation $ $
$y' = \color{#FF6800}{3x ^ {2}} + \dfrac{d}{dx}(- 2x) - \dfrac{d}{dx}(48)$
$y' = \color{#FF6800}{}3x ^ {2}\color{#FF6800}{ + \dfrac{d}{dx}(- 2x)} - \dfrac{d}{dx}(48)$
$ $ Calculate the differentiation $ $
$y' = \color{#FF6800}{}3x ^ {2}\color{#FF6800}{ - 2} - \dfrac{d}{dx}(48)$
$y' = 3x ^ {2} - 2 - \color{#FF6800}{\dfrac{d}{dx}(48)}$
$ $ Calculate the differentiation $ $
$y' = 3x ^ {2} - 2 - \color{#FF6800}{0}$
$y' = \color{#FF6800}{}3x ^ {2} - 2\color{#FF6800}{ - 0}$
$ $ Solve the formula $ $
$y' = 3x ^ {2} - 2$
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