What is the inflection f(x)= 1/4 x^4-2x^2 ?

The inflection f(x)= 1/4 x^4-2x^2 is (-2/(sqrt(3)),-20/9),(2/(sqrt(3)),-20/9)

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inflection f(x)= 1/4 x^4-2x^2

inflection points

f (x) = \frac{1}{4} x^{4} - 2 x^{2}

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

Solution steps

f^{''} (x) = 3 x^{2} - 4

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

\frac{1}{4} x^{4} - 2 x^{2} : - \frac{20}{9}

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

Plug

x = \frac{2}{3}

into

\frac{1}{4} x^{4} - 2 x^{2} : - \frac{20}{9}

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

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

f (x) = 2 x^{3} - x^{2} - 4 x + 3

f (x) = \frac{1}{4} x^{2} - 3

f (x) = \frac{1}{2 x - 10}

f (x) = \frac{x + 5}{x + 7}

f (x) = \frac{5 x - 3}{2 x + 1}

What is the inflection f(x)= 1/4 x^4-2x^2 ?
The inflection f(x)= 1/4 x^4-2x^2 is (-2/(sqrt(3)),-20/9),(2/(sqrt(3)),-20/9)