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

The inflection f(x)=x^4-2x^2+2 is (-1/(sqrt(3)), 13/9),(1/(sqrt(3)), 13/9)

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

inflection points

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

(- \frac{1}{3}, \frac{13}{9}), (\frac{1}{3}, \frac{13}{9})

Solution steps

f^{''} (x) = 12 x^{2} - 4

Find intervals:

Concave Upward

: - \infty < x < - \frac{1}{3},

Concave Downward

: - \frac{1}{3} < x < \frac{1}{3},

Concave Upward

: \frac{1}{3} < x < \infty

Plug

x = - \frac{1}{3}

into

x^{4} - 2 x^{2} + 2 : \frac{13}{9}

(- \frac{1}{3}, \frac{13}{9})

Plug

x = \frac{1}{3}

into

x^{4} - 2 x^{2} + 2 : \frac{13}{9}

(\frac{1}{3}, \frac{13}{9})

(- \frac{1}{3}, \frac{13}{9}), (\frac{1}{3}, \frac{13}{9})

f (x) = 2 x^{5} + 16 x^{4} - 6 x^{3} - 48 x^{2}

f (x) = \frac{x + sin ( x π )}{x + 1}

f (x) = - x - 1

\frac{2 x + 3}{x + 1}

f (x) = 80 - 0.2 x

What is the inflection f(x)=x^4-2x^2+2 ?
The inflection f(x)=x^4-2x^2+2 is (-1/(sqrt(3)), 13/9),(1/(sqrt(3)), 13/9)