What is the inflection f(x)=3x^4-6x^2+2/3 ?

The inflection f(x)=3x^4-6x^2+2/3 is (-1/(sqrt(3)),-1),(1/(sqrt(3)),-1)

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inflection f(x)=3x^4-6x^2+2/3

inflection points

f (x) = 3 x^{4} - 6 x^{2} + \frac{2}{3}

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

Solution steps

f^{''} (x) = 36 x^{2} - 12

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

3 x^{4} - 6 x^{2} + \frac{2}{3} : - 1

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

Plug

x = \frac{1}{3}

into

3 x^{4} - 6 x^{2} + \frac{2}{3} : - 1

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

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

f (x) = \frac{( 2 + x )}{( x + 5 ) ( x + 7 )}

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

x (x + 11) (x - 6)

f (x) = 7 x - 5

y = - 2 x + 7

What is the inflection f(x)=3x^4-6x^2+2/3 ?
The inflection f(x)=3x^4-6x^2+2/3 is (-1/(sqrt(3)),-1),(1/(sqrt(3)),-1)