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Formula
Calculate the differentiation
Find the points of local maxima, local minima and the points of inflection of the function
Graph
$f \left( x \right) = 2 x ^ { 2 } - 4 x - 1$
$x$Intercept
$\left ( 1 - \dfrac { \sqrt{ 6 } } { 2 } , 0 \right )$, $\left ( 1 + \dfrac { \sqrt{ 6 } } { 2 } , 0 \right )$
$f \left( x \right)$Intercept
$\left ( 0 , - 1 \right )$
Minimum
$\left ( 1 , - 3 \right )$
Standard form
$f \left( x \right) = 2 \left ( x - 1 \right ) ^ { 2 } - 3$
$f\left( x \right) = 2x ^{ 2 } -4x-1$
$\dfrac {d } {d x } {\left( f \left( x \right) \right)} = 4 x - 4$
Calculate the differentiation of the logarithmic function
$\dfrac {d } {d \color{#FF6800}{ x } } {\left( \color{#FF6800}{ 2 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right)}$
 Calculate the differentiation 
$\color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 4 }$
$x = 1 ,$ minimal value 
Find the points of local maxima, local minima and the points of inflection of the function
$f \left( \color{#FF6800}{ x } \right) = \color{#FF6800}{ 2 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 }$
 Find critical points (Points where the differential value becomes 0) 
$\color{#FF6800}{ x } = \color{#FF6800}{ 1 }$
$\begin{cases} f \left( \color{#FF6800}{ x } \right) = \color{#FF6800}{ 2 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \\ \dfrac {d } {d \color{#FF6800}{ x } } {\left( f \right)} \left( \color{#FF6800}{ 1 } \right) = \color{#FF6800}{ 0 } \end{cases}$
 Determine if it is the maximal value, the minimal value, the increasing inflection point, or the decreasing inflection point 
 It is the minimal value 
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