What is the inflection f(x)=x^{2/5}(x-5) ?

The inflection f(x)=x^{2/5}(x-5) is (-15/7 ,-(50(-15/7)^{2/5})/7)

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inflection f(x)=x^{2/5}(x-5)

inflection points

f (x) = x^{\frac{2}{5}} (x - 5)

- \frac{15}{7}, - \frac{50 ( - \frac{15}{7} ) ^{\frac{2}{5}}}{7}

Solution steps

f^{''} (x) = \frac{14 x + 30}{25 x ^{\frac{8}{5}}}

Find intervals:

Concave Downward

: - \infty < x < - \frac{15}{7},

Concave Upward

: - \frac{15}{7} < x < 0,

Concave Upward

: 0 < x < \infty

Plug

x = - \frac{15}{7}

into

x^{\frac{2}{5}} (x - 5) : - \frac{50 ( - \frac{15}{7} ) ^{\frac{2}{5}}}{7}

- \frac{15}{7}, - \frac{50 ( - \frac{15}{7} ) ^{\frac{2}{5}}}{7}

What is the inflection f(x)=x^{2/5}(x-5) ?
The inflection f(x)=x^{2/5}(x-5) is (-15/7 ,-(50(-15/7)^{2/5})/7)