What is the inflection f(x)=x^4-16x^2 ?

The inflection f(x)=x^4-16x^2 is (-(2sqrt(2))/(sqrt(3)),-320/9),((2sqrt(2))/(sqrt(3)),-320/9)

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inflection f(x)=x^4-16x^2

inflection points

f (x) = x^{4} - 16 x^{2}

(- \frac{2 2}{3}, - \frac{320}{9}), (\frac{2 2}{3}, - \frac{320}{9})

Solution steps

f^{''} (x) = 12 x^{2} - 32

Find intervals:

Concave Upward

: - \infty < x < - \frac{2 2}{3},

Concave Downward

: - \frac{2 2}{3} < x < \frac{2 2}{3},

Concave Upward

: \frac{2 2}{3} < x < \infty

Plug

x = - \frac{2 2}{3}

into

x^{4} - 16 x^{2} : - \frac{320}{9}

(- \frac{2 2}{3}, - \frac{320}{9})

Plug

x = \frac{2 2}{3}

into

x^{4} - 16 x^{2} : - \frac{320}{9}

(\frac{2 2}{3}, - \frac{320}{9})

(- \frac{2 2}{3}, - \frac{320}{9}), (\frac{2 2}{3}, - \frac{320}{9})

\frac{x}{x}

f (x) = lo g_{\frac{1}{9}} (x)

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

x = 2

f (x) = 3 x + 5

What is the inflection f(x)=x^4-16x^2 ?
The inflection f(x)=x^4-16x^2 is (-(2sqrt(2))/(sqrt(3)),-320/9),((2sqrt(2))/(sqrt(3)),-320/9)