What is the inflection x^4-16x^2 ?

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

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inflection x^4-16x^2

inflection points

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 + 8}{x ^{2} - 5 x - 24}

3 cos (x - π)

sin (7 x), 0 \leq x \leq 2 π

f (x) = 5 (x + 8) - 4

- x^{2} + 10 x

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