What is the extreme x^{5/3}-5x^{2/3} ?

The extreme x^{5/3}-5x^{2/3} is Maximum(0,0),Minimum(2,-3*2^{2/3})

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extreme x^{5/3}-5x^{2/3}

extreme points

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

Maximum (0, 0), Minimum (2, - 3 \cdot 2^{\frac{2}{3}})

Solution steps

f^{'} (x) = \frac{5 x - 10}{3 x ^{\frac{1}{3}}}

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = 0

into

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

Maximum (0, 0)

Plug

x = 2

into

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

Minimum (2, - 3 \cdot 2^{\frac{2}{3}})

Maximum (0, 0), Minimum (2, - 3 \cdot 2^{\frac{2}{3}})

f (x, y) = x^{3} + 3 x y^{2} - 15 x + y^{3} - 15 y

f (x) = x + \frac{36}{x}

f (x) = \frac{x}{x ^{2} - x + 9}, 0 \leq x \leq 9

f (x) = e^{x^{2} - 3 x - 1}

f (x) = 3 x^{4} + 16 x^{3}

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