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Formula
Calculate the differentiation
Answer
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Find the points of local maxima, local minima and the points of inflection of the function
Answer
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Graph
$ f \left( x \right) = x ^ { 2 } + 1$
$ f \left( x \right)$Intercept
$\left ( 0 , 1 \right )$
Minimum
$\left ( 0 , 1 \right )$
Standard form
$ f \left( x \right) = x ^ { 2 } + 1$
$f\left( x \right) = x ^{ 2 } +1$
$\dfrac {d } {d x } {\left( f \left( x \right) \right)} = 2 x$
Calculate the differentiation of the logarithmic function
$\dfrac {d } {d \color{#FF6800}{ x } } {\left( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right)}$
$ $ Calculate the differentiation $ $
$\color{#FF6800}{ 2 } \color{#FF6800}{ x }$
$x = 0 , $ 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}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 }$
$ $ Find critical points (Points where the differential value becomes 0) $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 0 }$
$\begin{cases} f \left( \color{#FF6800}{ x } \right) = \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \\ \dfrac {d } {d \color{#FF6800}{ x } } {\left( f \right)} \left( \color{#FF6800}{ 0 } \right) = \color{#FF6800}{ 0 } \end{cases}$
$ $ 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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