What is the extreme f(x)=3x^{5/3}-2x^{2/3} ?

The extreme f(x)=3x^{5/3}-2x^{2/3} is Maximum(0,0),Minimum(4/15 ,3(4/15)^{5/3}-2(4/15)^{2/3})

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extreme f(x)=3x^{5/3}-2x^{2/3}

extreme

Maximum (0, 0), Minimum (\frac{4}{15}, 3 (\frac{4}{15})^{\frac{5}{3}} - 2 (\frac{4}{15})^{\frac{2}{3}})

Solution steps

f^{'} (x) = \frac{- 4 + 15 x}{3 x ^{\frac{1}{3}}}

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{4}{15},

Increasing

: \frac{4}{15} < x < \infty

Plug

x = 0

into

3 x^{\frac{5}{3}} - 2 x^{\frac{2}{3}} : 0

Maximum (0, 0)

Plug

x = \frac{4}{15}

into

3 x^{\frac{5}{3}} - 2 x^{\frac{2}{3}} : 3 (\frac{4}{15})^{\frac{5}{3}} - 2 (\frac{4}{15})^{\frac{2}{3}}

Minimum (\frac{4}{15}, 3 (\frac{4}{15})^{\frac{5}{3}} - 2 (\frac{4}{15})^{\frac{2}{3}})

Maximum (0, 0), Minimum (\frac{4}{15}, 3 (\frac{4}{15})^{\frac{5}{3}} - 2 (\frac{4}{15})^{\frac{2}{3}})

What is the extreme f(x)=3x^{5/3}-2x^{2/3} ?
The extreme f(x)=3x^{5/3}-2x^{2/3} is Maximum(0,0),Minimum(4/15 ,3(4/15)^{5/3}-2(4/15)^{2/3})