What is the inflection f(x)=x^{1/7}(x+8) ?

The inflection f(x)=x^{1/7}(x+8) is (0,0),(6,14*6^{1/7})

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inflection f(x)=x^{1/7}(x+8)

inflection points

f (x) = x^{\frac{1}{7}} (x + 8)

(0, 0), (6, 14 \cdot 6^{\frac{1}{7}})

Solution steps

f^{''} (x) = \frac{8 ( x - 6 )}{49 x ^{\frac{13}{7}}}

Find intervals:

Concave Upward

: - \infty < x < 0,

Concave Downward

: 0 < x < 6,

Concave Upward

: 6 < x < \infty

Plug

x = 0

into

x^{\frac{1}{7}} (x + 8) : 0

(0, 0)

Plug

x = 6

into

x^{\frac{1}{7}} (x + 8) : 14 \cdot 6^{\frac{1}{7}}

(6, 14 \cdot 6^{\frac{1}{7}})

(0, 0), (6, 14 \cdot 6^{\frac{1}{7}})

What is the inflection f(x)=x^{1/7}(x+8) ?
The inflection f(x)=x^{1/7}(x+8) is (0,0),(6,14*6^{1/7})