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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) = \left ( x ^ { 2 } - 2 \right ) ^ { 2 }$
$x$Intercept
$\left ( - \sqrt{ 2 } , 0 \right )$, $\left ( \sqrt{ 2 } , 0 \right )$
$ f \left( x \right)$Intercept
$\left ( 0 , 4 \right )$
Derivative
$4 x ^ { 3 } - 8 x$
Seconde derivative
$12 x ^ { 2 } - 8$
Local Minimum
$\left ( - \sqrt{ 2 } , 0 \right )$, $\left ( \sqrt{ 2 } , 0 \right )$
Local Maximum
$\left ( 0 , 4 \right )$
Point of inflection
$\left ( - \dfrac { \sqrt{ 6 } } { 3 } , \dfrac { 16 } { 9 } \right )$, $\left ( \dfrac { \sqrt{ 6 } } { 3 } , \dfrac { 16 } { 9 } \right )$
$f \left( x \right) = \left( x ^{ 2 } -2 \right) ^{ 2 }$
$\dfrac {d } {d x } {\left( f \left( x \right) \right)} = 4 x ^ { 3 } - 8 x$
Calculate the differentiation of the logarithmic function
$\dfrac {d } {d \color{#FF6800}{ x } } {\left( \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) ^ { \color{#FF6800}{ 2 } } \right)}$
$ $ Calculate the differentiation $ $
$\color{#FF6800}{ 4 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 8 } \color{#FF6800}{ x }$
$x = - \sqrt{ 2 } , $ minimal value $ \\ x = 0 , $ maximal value $ \\ x = \sqrt{ 2 } , $ minimal value $ $
Find the points of local maxima, local minima and the points of inflection of the function
$ f \left( \color{#FF6800}{ x } \right) = \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) ^ { \color{#FF6800}{ 2 } }$
$ $ Find critical points (Points where the differential value becomes 0) $ $
$\begin{array} {l} \color{#FF6800}{ x } = \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } \\ \color{#FF6800}{ x } = \color{#FF6800}{ 0 } \\ \color{#FF6800}{ x } = \sqrt{ \color{#FF6800}{ 2 } } \end{array}$
$\begin{cases} f \left( \color{#FF6800}{ x } \right) = \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) ^ { \color{#FF6800}{ 2 } } \\ \dfrac {d } {d \color{#FF6800}{ x } } {\left( f \right)} \left( \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } \right) = \color{#FF6800}{ 0 } \end{cases}$
$ $ Determine if it is the maximal value, the minimal value, the increasing inflection point, or the decreasing inflection point $ $
$ $ It is the minimal value $ $
$\begin{cases} f \left( \color{#FF6800}{ x } \right) = \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) ^ { \color{#FF6800}{ 2 } } \\ \dfrac {d } {d \color{#FF6800}{ x } } {\left( f \right)} \left( \color{#FF6800}{ 0 } \right) = \color{#FF6800}{ 0 } \end{cases}$
$ $ Determine if it is the maximal value, the minimal value, the increasing inflection point, or the decreasing inflection point $ $
$ $ It is the maximal value $ $
$\begin{cases} f \left( \color{#FF6800}{ x } \right) = \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) ^ { \color{#FF6800}{ 2 } } \\ \dfrac {d } {d \color{#FF6800}{ x } } {\left( f \right)} \left( \sqrt{ \color{#FF6800}{ 2 } } \right) = \color{#FF6800}{ 0 } \end{cases}$
$ $ Determine if it is the maximal value, the minimal value, the increasing inflection point, or the decreasing inflection point $ $
$ $ It is the minimal value $ $
$ $ 그래프 보기 $ $
Higher order function
Solution search results
search-thumbnail-If the sum of two consecutive 
numbers is $45$ and one number is $X$ 
.This statement in the form of 
equation $1s:$ 
$\left(1$ Point) $\right)$ 
$○5x+1$ $1eft\left(x+1$ $r1gnt\right)=45s$ 
$○sx+1ef\left(x+2$ $r1gnt\right)=145s$ 
$sx+1x=45s$
7th-9th grade
Algebra
search-thumbnail-$s|ef\left(-1n$ $\left($ }\right)^{50}\ $\right)$ \ | | is\ equal\ to\ $S$ 
$s1S$ 
$S-1S$ 
$s2S$ 
$s50s$
7th-9th grade
Other
search-thumbnail-Given the set of ordered pairs $\left(\left(-7.0\right),\left(-6,5\right),\left(-5,-3\right),\left(-1,2\right)$ $\left(1,6\right),\left(2,-2\right)$ $\left(5,3\right)\left(7,-8\right)\right)$ 
Find f(7)fAleft(7\right) 
O a 
O b -8 
6. 
$5$
7th-9th grade
Algebra
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