What is the extreme 2x^{5/3}-5x^{4/3} ?

The extreme 2x^{5/3}-5x^{4/3} is Maximum(0,0),Minimum(8,-16)

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extreme 2x^{5/3}-5x^{4/3}

extreme points

2 x^{\frac{5}{3}} - 5 x^{\frac{4}{3}}

Maximum (0, 0), Minimum (8, - 16)

Solution steps

f^{'} (x) = \frac{10 x ^{\frac{2}{3}} - 20 x ^{\frac{1}{3}}}{3}

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 8,

Increasing

: 8 < x < \infty

Plug

x = 0

into

2 x^{\frac{5}{3}} - 5 x^{\frac{4}{3}} : 0

Maximum (0, 0)

Plug

x = 8

into

2 x^{\frac{5}{3}} - 5 x^{\frac{4}{3}} : - 16

Minimum (8, - 16)

Maximum (0, 0), Minimum (8, - 16)

f (x) = \frac{1}{3} x^{3} + \frac{3}{2} x^{2} - 4 x

\frac{d}{d x} ((x + y) 2 + 2 y^{2})

f (x) = \frac{2 ( x + 7 ) ^{2}}{x + 10}

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

f (x) = 2 x^{2} - 12 x + 20

What is the extreme 2x^{5/3}-5x^{4/3} ?
The extreme 2x^{5/3}-5x^{4/3} is Maximum(0,0),Minimum(8,-16)