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

The extreme f(x)=5x^{2/3}-2x^{5/3} is Minimum(0,0),Maximum(1,3)

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

extreme points

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

Minimum (0, 0), Maximum (1, 3)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = 0

into

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

Minimum (0, 0)

Plug

x = 1

into

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

Maximum (1, 3)

Minimum (0, 0), Maximum (1, 3)

f (x) = ln (x^{2} + x + 1)

f (x) = x^{2} - 4 x y + y^{3} + 4 y

V, V = 13 π r 2 h

f (x) = x^{3} + 3 x y + y^{3}

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

What is the extreme f(x)=5x^{2/3}-2x^{5/3} ?
The extreme f(x)=5x^{2/3}-2x^{5/3} is Minimum(0,0),Maximum(1,3)