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

The inflection f(x)=x(x-3sqrt(x)) is (81/64 ,-10935/4096)

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inflection f(x)=x(x-3sqrt(x))

inflection points

f (x) = x (x - 3 x)

(\frac{81}{64}, - \frac{10935}{4096})

Solution steps

f^{''} (x) = \frac{1}{2} (4 - \frac{9}{2 x})

Find intervals:

Concave Downward

: 0 < x < \frac{81}{64},

Concave Upward

: \frac{81}{64} < x < \infty

Plug

x = \frac{81}{64}

into

x (x - 3 x) : - \frac{10935}{4096}

(\frac{81}{64}, - \frac{10935}{4096})

What is the inflection f(x)=x(x-3sqrt(x)) ?
The inflection f(x)=x(x-3sqrt(x)) is (81/64 ,-10935/4096)