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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
$f \left( x \right) = x ^ { 5 }$
$x$Intercept
$\left ( 0 , 0 \right )$
$f \left( x \right)$Intercept
$\left ( 0 , 0 \right )$
Derivative
$5 x ^ { 4 }$
Seconde derivative
$20 x ^ { 3 }$
Local Maximum
$\left ( 0 , 0 \right )$
Point of inflection
$\left ( 0 , 0 \right )$
$f \left( x \right) = x ^{ 5 }$
$\dfrac {d } {d x } {\left( f \left( x \right) \right)} = 5 x ^ { 4 }$
Calculate the differentiation of the logarithmic function
$\dfrac {d } {d \color{#FF6800}{ x } } {\left( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 5 } } \right)}$
 Calculate the differentiation 
$\color{#FF6800}{ 5 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 4 } }$
$x = 0 ,$ increasing inflection point 
Find the points of local maxima, local minima and the points of inflection of the function
$f \left( \color{#FF6800}{ x } \right) = \color{#FF6800}{ x } ^ { \color{#FF6800}{ 5 } }$
 Find critical points (Points where the differential value becomes 0) 
$\color{#FF6800}{ x } = \color{#FF6800}{ 0 }$
$\begin{cases} f \left( \color{#FF6800}{ x } \right) = \color{#FF6800}{ x } ^ { \color{#FF6800}{ 5 } } \\ \dfrac {d } {d \color{#FF6800}{ x } } {\left( f \right)} \left( \color{#FF6800}{ 0 } \right) = \color{#FF6800}{ 0 } \end{cases}$
 Determine if it is the maximal value, the minimal value, the increasing inflection point, or the decreasing inflection point 
 It is the increasing inflection point 
 그래프 보기 
Higher order function
Solution search results