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

The inflection f(x)=3x^4-6x^2 is (-1/(sqrt(3)),-5/3),(1/(sqrt(3)),-5/3)

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

inflection points

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

(- \frac{1}{3}, - \frac{5}{3}), (\frac{1}{3}, - \frac{5}{3})

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{5}{3}

(- \frac{1}{3}, - \frac{5}{3})

Plug

x = \frac{1}{3}

into

3 x^{4} - 6 x^{2} : - \frac{5}{3}

(\frac{1}{3}, - \frac{5}{3})

(- \frac{1}{3}, - \frac{5}{3}), (\frac{1}{3}, - \frac{5}{3})

What is the inflection f(x)=3x^4-6x^2 ?
The inflection f(x)=3x^4-6x^2 is (-1/(sqrt(3)),-5/3),(1/(sqrt(3)),-5/3)