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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
$y = \left ( x + 2 \right ) ^ { 2 } + 3$
$y$Intercept
$\left ( 0 , 7 \right )$
Minimum
$\left ( - 2 , 3 \right )$
Standard form
$y = \left ( x + 2 \right ) ^ { 2 } + 3$
$y = \left( x+2 \right) ^{ 2 } +3$
$3$
Find the maximum and minimum of the quadratic function
$\color{#FF6800}{ y } = \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 }$
$ $ As $ a \gt 0 $ is, the minimum value is $ 3 $ if $ x = - 2$
$\color{#FF6800}{ 3 }$
$\dfrac {d } {d x } {\left( y \right)} = 2 x + 4$
Calculate the differentiation of the logarithmic function
$\dfrac {d } {d \color{#FF6800}{ x } } {\left( \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right)}$
$ $ Calculate the differentiation $ $
$\color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 4 }$
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