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

The inflection f(x)=(x-2)^2(x-4)^2 is ((9-sqrt(3))/3 ,-572/9+64),((9+sqrt(3))/3 ,-572/9+64)

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

inflection points

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

(\frac{9 - 3}{3}, - \frac{572}{9} + 64), (\frac{9 + 3}{3}, - \frac{572}{9} + 64)

Solution steps

f^{''} (x) = 4 (3 x^{2} - 18 x + 26)

Find intervals:

Concave Upward

: - \infty < x < - \frac{1}{3} + 3,

Concave Downward

: - \frac{1}{3} + 3 < x < \frac{1}{3} + 3,

Concave Upward

: \frac{1}{3} + 3 < x < \infty

Plug

x = \frac{9 - 3}{3}

into

(x - 2)^{2} (x - 4)^{2} : - \frac{572}{9} + 64

(\frac{9 - 3}{3}, - \frac{572}{9} + 64)

Plug

x = \frac{9 + 3}{3}

into

(x - 2)^{2} (x - 4)^{2} : - \frac{572}{9} + 64

(\frac{9 + 3}{3}, - \frac{572}{9} + 64)

(\frac{9 - 3}{3}, - \frac{572}{9} + 64), (\frac{9 + 3}{3}, - \frac{572}{9} + 64)

What is the inflection f(x)=(x-2)^2(x-4)^2 ?
The inflection f(x)=(x-2)^2(x-4)^2 is ((9-sqrt(3))/3 ,-572/9+64),((9+sqrt(3))/3 ,-572/9+64)