What is the extreme f(x)=-5x^{5/3}+5\sqrt[3]{x} ?

The extreme f(x)=-5x^{5/3}+5\sqrt[3]{x} is

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extreme f(x)=-5x^{5/3}+5\sqrt[3]{x}

extreme

Minimum (- \frac{1}{5 ^{\frac{3}{4}}}, - 5 (- \frac{1}{5 ^{\frac{3}{4}}})^{\frac{5}{3}} - 5 (\frac{1}{5 ^{\frac{3}{4}}})^{\frac{1}{3}}), Maximum (\frac{1}{5 ^{\frac{3}{4}}}, - 5 (\frac{1}{5 ^{\frac{3}{4}}})^{\frac{5}{3}} + 5 3 \frac{1}{5 ^{\frac{3}{4}}})

Solution steps

f^{'} (x) = - \frac{25 x ^{\frac{2}{3}}}{3} + \frac{5}{3 x ^{\frac{2}{3}}}

Find intervals:

Decreasing

: - \infty < x < - \frac{1}{5 ^{\frac{3}{4}}},

Increasing

: - \frac{1}{5 ^{\frac{3}{4}}} < x < 0,

Increasing

: 0 < x < \frac{1}{5 ^{\frac{3}{4}}},

Decreasing

: \frac{1}{5 ^{\frac{3}{4}}} < x < \infty

Plug

x = - \frac{1}{5 ^{\frac{3}{4}}}

into

- 5 x^{\frac{5}{3}} + 5 3 x : - 5 (- \frac{1}{5 ^{\frac{3}{4}}})^{\frac{5}{3}} - 5 (\frac{1}{5 ^{\frac{3}{4}}})^{\frac{1}{3}}

Minimum (- \frac{1}{5 ^{\frac{3}{4}}}, - 5 (- \frac{1}{5 ^{\frac{3}{4}}})^{\frac{5}{3}} - 5 (\frac{1}{5 ^{\frac{3}{4}}})^{\frac{1}{3}})

Plug

x = \frac{1}{5 ^{\frac{3}{4}}}

into

- 5 x^{\frac{5}{3}} + 5 3 x : - 5 (\frac{1}{5 ^{\frac{3}{4}}})^{\frac{5}{3}} + 5 3 \frac{1}{5 ^{\frac{3}{4}}}

Maximum (\frac{1}{5 ^{\frac{3}{4}}}, - 5 (\frac{1}{5 ^{\frac{3}{4}}})^{\frac{5}{3}} + 5 3 \frac{1}{5 ^{\frac{3}{4}}})

Minimum (- \frac{1}{5 ^{\frac{3}{4}}}, - 5 (- \frac{1}{5 ^{\frac{3}{4}}})^{\frac{5}{3}} - 5 (\frac{1}{5 ^{\frac{3}{4}}})^{\frac{1}{3}}), Maximum (\frac{1}{5 ^{\frac{3}{4}}}, - 5 (\frac{1}{5 ^{\frac{3}{4}}})^{\frac{5}{3}} + 5 3 \frac{1}{5 ^{\frac{3}{4}}})

What is the extreme f(x)=-5x^{5/3}+5\sqrt[3]{x} ?
The extreme f(x)=-5x^{5/3}+5\sqrt[3]{x} is