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Formula
Find the maximum and minimum of the quadratic function
Answer
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Calculate the differentiation
Answer
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Graph
$y = x ^ { 2 } - 2$
$x$Intercept
$\left ( \sqrt{ 2 } , 0 \right )$, $\left ( - \sqrt{ 2 } , 0 \right )$
$y$Intercept
$\left ( 0 , - 2 \right )$
Minimum
$\left ( 0 , - 2 \right )$
Standard form
$y = x ^ { 2 } - 2$
$y = x ^{ 2 } -2$
$- 2$
Find the maximum and minimum of the quadratic function
$\color{#FF6800}{ y } = \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 }$
$ $ As $ a \gt 0 $ is, the minimum value is $ - 2 $ if $ x = 0$
$\color{#FF6800}{ - } \color{#FF6800}{ 2 }$
$\dfrac {d } {d x } {\left( y \right)} = 2 x$
Calculate the differentiation of the logarithmic function
$\dfrac {d } {d \color{#FF6800}{ x } } {\left( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right)}$
$ $ Calculate the differentiation $ $
$\color{#FF6800}{ 2 } \color{#FF6800}{ x }$
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