What is the extreme f(x)=x^{1/3}(x+3)^{2/3} ?

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

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extreme f(x)=x^{1/3}(x+3)^{2/3}

extreme points

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

Maximum (- 3, 0), Minimum (- 1, - 2^{\frac{2}{3}})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < - 1,

Increasing

: - 1 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 3

into

x^{\frac{1}{3}} (x + 3)^{\frac{2}{3}} : 0

Maximum (- 3, 0)

Plug

x = - 1

into

x^{\frac{1}{3}} (x + 3)^{\frac{2}{3}} : - 2^{\frac{2}{3}}

Minimum (- 1, - 2^{\frac{2}{3}})

Maximum (- 3, 0), Minimum (- 1, - 2^{\frac{2}{3}})

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

f (x) = x^{4} - 8 x^{2} + 8

f (x) = 6 x^{4} + 2 x^{3} - 12 x^{2} + 3

f (x, y) = x y + \frac{64}{x} + \frac{64}{y}

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

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