What is the inflection y=x^4-4x^2 ?

The inflection y=x^4-4x^2 is (-sqrt(2/3),-20/9),(sqrt(2/3),-20/9)

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inflection y=x^4-4x^2

inflection points

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

(- \frac{2}{3}, - \frac{20}{9}), (\frac{2}{3}, - \frac{20}{9})

Solution steps

f^{''} (x) = 12 x^{2} - 8

Find intervals:

Concave Upward

: - \infty < x < - \frac{2}{3},

Concave Downward

: - \frac{2}{3} < x < \frac{2}{3},

Concave Upward

: \frac{2}{3} < x < \infty

Plug

x = - \frac{2}{3}

into

x^{4} - 4 x^{2} : - \frac{20}{9}

(- \frac{2}{3}, - \frac{20}{9})

Plug

x = \frac{2}{3}

into

x^{4} - 4 x^{2} : - \frac{20}{9}

(\frac{2}{3}, - \frac{20}{9})

(- \frac{2}{3}, - \frac{20}{9}), (\frac{2}{3}, - \frac{20}{9})

\frac{4 x}{9 x - 1}

(1.2) (5.8)

sec^{2} (2 x) d x

y = x e^{- 2 x^{2}}

f (x) = \frac{1 + 3 x ^{2} - x ^{3}}{x ^{2}}

What is the inflection y=x^4-4x^2 ?
The inflection y=x^4-4x^2 is (-sqrt(2/3),-20/9),(sqrt(2/3),-20/9)