What is the inflection f(x)=x^4-4x^2 ?

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

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inflection f(x)=x^4-4x^2

inflection points

f (x) = 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})

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