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

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

inflection points

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

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

Solution steps

f^{''} (x) = 4 (3 x^{2} - 12 x + 8)

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})

- x + 5 + (x + 2) (x - 2)

(3, - 4), (- 1, 10)

y = ln (2 x)

f (x) = 6 x - 2 y = 12

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

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