What is the inflection f(x)=x^2(5-4x)^2 ?

The inflection f(x)=x^2(5-4x)^2 is ((5(3-sqrt(3)))/(24), 625/576),((5(3+sqrt(3)))/(24), 625/576)

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inflection f(x)=x^2(5-4x)^2

inflection points

f (x) = x^{2} (5 - 4 x)^{2}

(\frac{5 ( 3 - 3 )}{24}, \frac{625}{576}), (\frac{5 ( 3 + 3 )}{24}, \frac{625}{576})

Solution steps

f^{''} (x) = 2 (96 x^{2} - 120 x + 25)

Find intervals:

Concave Upward

: - \infty < x < - \frac{5}{8 3} + \frac{5}{8},

Concave Downward

: - \frac{5}{8 3} + \frac{5}{8} < x < \frac{5}{8 3} + \frac{5}{8},

Concave Upward

: \frac{5}{8 3} + \frac{5}{8} < x < \infty

Plug

x = \frac{5 ( 3 - 3 )}{24}

into

x^{2} (5 - 4 x)^{2} : \frac{625}{576}

(\frac{5 ( 3 - 3 )}{24}, \frac{625}{576})

Plug

x = \frac{5 ( 3 + 3 )}{24}

into

x^{2} (5 - 4 x)^{2} : \frac{625}{576}

(\frac{5 ( 3 + 3 )}{24}, \frac{625}{576})

(\frac{5 ( 3 - 3 )}{24}, \frac{625}{576}), (\frac{5 ( 3 + 3 )}{24}, \frac{625}{576})

y = - 3 x^{2} - 24 x - 42

x^{2} + 4 x - 12

(100, 0), (0, - 20)

\frac{- x ^{2}}{x + 1}

f (x) = \frac{x ^{\frac{1}{2}}}{4}

What is the inflection f(x)=x^2(5-4x)^2 ?
The inflection f(x)=x^2(5-4x)^2 is ((5(3-sqrt(3)))/(24), 625/576),((5(3+sqrt(3)))/(24), 625/576)