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$y = x ^ { 4 } - x ^ { 2 } - 20$

$y = 0$

$x$-intercept

$\left ( \sqrt{ 5 } , 0 \right )$, $\left ( - \sqrt{ 5 } , 0 \right )$

$y$-intercept

$\left ( 0 , - 20 \right )$

Derivative

$4 x ^ { 3 } - 2 x$

Seconde derivative

$12 x ^ { 2 } - 2$

Local Minimum

$\left ( - \dfrac { \sqrt{ 2 } } { 2 } , - \dfrac { 81 } { 4 } \right )$, $\left ( \dfrac { \sqrt{ 2 } } { 2 } , - \dfrac { 81 } { 4 } \right )$

Local Maximum

$\left ( 0 , - 20 \right )$

Point of inflection

$\left ( - \dfrac { \sqrt{ 6 } } { 6 } , - \dfrac { 725 } { 36 } \right )$, $\left ( \dfrac { \sqrt{ 6 } } { 6 } , - \dfrac { 725 } { 36 } \right )$

$x ^{ 4 } -x ^{ 2 } -20 = 0$

$ $ 그래프 보기 $ $

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1st-6th grade

Algebra

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