What is the extreme f(x)=x^{1/5}(x+3) ?

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

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extreme f(x)=x^{1/5}(x+3)

extreme points

f (x) = x^{\frac{1}{5}} (x + 3)

Minimum (- \frac{1}{2}, - \frac{5}{2 \cdot 2 ^{\frac{1}{5}}})

Solution steps

f^{'} (x) = \frac{3 ( 2 x + 1 )}{5 x ^{\frac{4}{5}}}

Find intervals:

Decreasing

: - \infty < x < - \frac{1}{2},

Increasing

: - \frac{1}{2} < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - \frac{1}{2}

into

x^{\frac{1}{5}} (x + 3) : - \frac{5}{2 \cdot 2 ^{\frac{1}{5}}}

Minimum (- \frac{1}{2}, - \frac{5}{2 \cdot 2 ^{\frac{1}{5}}})

x^{3} + 3 x^{2} + 1

f (x) = - 5 x^{4} + 5 x^{3} - 10

f (x, y) = 3 x^{- 2} + 5 y^{- 2} + 8 x y^{2}

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

f (x) = ln (x + y)

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