What is the inflection f(x)=x(8-x)^{1/3} ?

The inflection f(x)=x(8-x)^{1/3} is (8,0),(12,-12*4^{1/3})

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inflection f(x)=x(8-x)^{1/3}

inflection points

f (x) = x (8 - x)^{\frac{1}{3}}

(8, 0), (12, - 12 \cdot 4^{\frac{1}{3}})

Solution steps

f^{''} (x) = - \frac{4 ( - x + 12 )}{9 ( 8 - x ) ^{\frac{5}{3}}}

Find intervals:

Concave Downward

: - \infty < x < 8,

Concave Upward

: 8 < x < 12,

Concave Downward

: 12 < x < \infty

Plug

x = 8

into

x (8 - x)^{\frac{1}{3}} : 0

(8, 0)

Plug

x = 12

into

x (8 - x)^{\frac{1}{3}} : - 12 \cdot 4^{\frac{1}{3}}

(12, - 12 \cdot 4^{\frac{1}{3}})

(8, 0), (12, - 12 \cdot 4^{\frac{1}{3}})

What is the inflection f(x)=x(8-x)^{1/3} ?
The inflection f(x)=x(8-x)^{1/3} is (8,0),(12,-12*4^{1/3})