What is the inflection f(x)=x^{1/3}(x-4) ?

The inflection f(x)=x^{1/3}(x-4) is (-2,6*2^{1/3}),(0,0)

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inflection f(x)=x^{1/3}(x-4)

inflection

(- 2, 6 \cdot 2^{\frac{1}{3}}), (0, 0)

Solution steps

f^{''} (x) = \frac{4 ( x + 2 )}{9 x ^{\frac{5}{3}}}

Find intervals:

Concave Upward

: - \infty < x < - 2,

Concave Downward

: - 2 < x < 0,

Concave Upward

: 0 < x < \infty

Plug

x = - 2

into

x^{\frac{1}{3}} (x - 4) : 6 \cdot 2^{\frac{1}{3}}

(- 2, 6 \cdot 2^{\frac{1}{3}})

Plug

x = 0

into

x^{\frac{1}{3}} (x - 4) : 0

(0, 0)

(- 2, 6 \cdot 2^{\frac{1}{3}}), (0, 0)

What is the inflection f(x)=x^{1/3}(x-4) ?
The inflection f(x)=x^{1/3}(x-4) is (-2,6*2^{1/3}),(0,0)