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

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

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

inflection points

f (x) = x^{\frac{1}{3}} (x + 4)

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

Solution steps

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

Find intervals:

Concave Upward

: - \infty < x < 0,

Concave Downward

: 0 < x < 2,

Concave Upward

: 2 < x < \infty

Plug

x = 0

into

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

(0, 0)

Plug

x = 2

into

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

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

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

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