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

The inflection (x^2-4)^4 is (-2/(sqrt(7)), 331776/2401),(2/(sqrt(7)), 331776/2401)

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inflection (x^2-4)^4

inflection points

(x^{2} - 4)^{4}

(- \frac{2}{7}, \frac{331776}{2401}), (\frac{2}{7}, \frac{331776}{2401})

Solution steps

f^{''} (x) = 8 ((x^{2} - 4)^{3} + 6 x^{2} (x^{2} - 4)^{2})

Find intervals:

Concave Upward

: - \infty < x < - 2,

Concave Upward

: - 2 < x < - \frac{2}{7},

Concave Downward

: - \frac{2}{7} < x < \frac{2}{7},

Concave Upward

: \frac{2}{7} < x < 2,

Concave Upward

: 2 < x < \infty

Plug

x = - \frac{2}{7}

into

(x^{2} - 4)^{4} : \frac{331776}{2401}

(- \frac{2}{7}, \frac{331776}{2401})

Plug

x = \frac{2}{7}

into

(x^{2} - 4)^{4} : \frac{331776}{2401}

(\frac{2}{7}, \frac{331776}{2401})

(- \frac{2}{7}, \frac{331776}{2401}), (\frac{2}{7}, \frac{331776}{2401})

f (x) = 4 x

x^{2} - x - 30

\frac{2}{3} (x - 2)^{2} - 5

f (x) = \frac{- 3 x ^{2} + 8 x}{3 x + 4}

15 x^{\frac{2}{3}} - 10 x

What is the inflection (x^2-4)^4 ?
The inflection (x^2-4)^4 is (-2/(sqrt(7)), 331776/2401),(2/(sqrt(7)), 331776/2401)