What is the inflection f(x)=x(x-9sqrt(x)) ?

The inflection f(x)=x(x-9sqrt(x)) is (729/64 ,-885735/4096)

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inflection f(x)=x(x-9sqrt(x))

inflection points

f (x) = x (x - 9 x)

(\frac{729}{64}, - \frac{885735}{4096})

Solution steps

f^{''} (x) = \frac{1}{2} (4 - \frac{27}{2 x})

Find intervals:

Concave Downward

: 0 < x < \frac{729}{64},

Concave Upward

: \frac{729}{64} < x < \infty

Plug

x = \frac{729}{64}

into

x (x - 9 x) : - \frac{885735}{4096}

(\frac{729}{64}, - \frac{885735}{4096})

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

(2, - 16), (- 7, - 3)

\frac{x ^{2} + 2 x + 1}{2 x ^{2} - x - 3}

f (x) = \frac{3 x - 3}{x ^{2} - 1}

What is the inflection f(x)=x(x-9sqrt(x)) ?
The inflection f(x)=x(x-9sqrt(x)) is (729/64 ,-885735/4096)