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

The inflection f(x)=(x^2-4x)^2 is ((2(3-sqrt(3)))/3 , 64/9),((2(3+sqrt(3)))/3 , 64/9)

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

inflection

(\frac{2 ( 3 - 3 )}{3}, \frac{64}{9}), (\frac{2 ( 3 + 3 )}{3}, \frac{64}{9})

Solution steps

f^{''} (x) = 2 (6 x^{2} - 24 x + 16)

Find intervals:

Concave Upward

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

Concave Downward

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

Concave Upward

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

Plug

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

into

(x^{2} - 4 x)^{2} : \frac{64}{9}

(\frac{2 ( 3 - 3 )}{3}, \frac{64}{9})

Plug

x = \frac{2 ( 3 + 3 )}{3}

into

(x^{2} - 4 x)^{2} : \frac{64}{9}

(\frac{2 ( 3 + 3 )}{3}, \frac{64}{9})

(\frac{2 ( 3 - 3 )}{3}, \frac{64}{9}), (\frac{2 ( 3 + 3 )}{3}, \frac{64}{9})

What is the inflection f(x)=(x^2-4x)^2 ?
The inflection f(x)=(x^2-4x)^2 is ((2(3-sqrt(3)))/3 , 64/9),((2(3+sqrt(3)))/3 , 64/9)