What is the inflection f(x)=x^2(3-x)^2 ?

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

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inflection f(x)=x^2(3-x)^2

inflection

(\frac{3 - 3}{2}, \frac{9}{4}), (\frac{3 + 3}{2}, \frac{9}{4})

Solution steps

f^{''} (x) = 2 (6 x^{2} - 18 x + 9)

Find intervals:

Concave Upward

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

Concave Downward

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

Concave Upward

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

Plug

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

into

x^{2} (3 - x)^{2} : \frac{9}{4}

(\frac{3 - 3}{2}, \frac{9}{4})

Plug

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

into

x^{2} (3 - x)^{2} : \frac{9}{4}

(\frac{3 + 3}{2}, \frac{9}{4})

(\frac{3 - 3}{2}, \frac{9}{4}), (\frac{3 + 3}{2}, \frac{9}{4})

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