What is the extreme f(x)=x^{4/5}(x+3) ?

The extreme f(x)=x^{4/5}(x+3) is Maximum(-4/3 ,(5(-4/3)^{4/5})/3),Minimum(0,0)

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extreme f(x)=x^{4/5}(x+3)

extreme points

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

Maximum - \frac{4}{3}, \frac{5 ( - \frac{4}{3} ) ^{\frac{4}{5}}}{3}, Minimum (0, 0)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - \frac{4}{3},

Decreasing

: - \frac{4}{3} < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - \frac{4}{3}

into

x^{\frac{4}{5}} (x + 3) : \frac{5 ( - \frac{4}{3} ) ^{\frac{4}{5}}}{3}

Maximum - \frac{4}{3}, \frac{5 ( - \frac{4}{3} ) ^{\frac{4}{5}}}{3}

Plug

x = 0

into

x^{\frac{4}{5}} (x + 3) : 0

Minimum (0, 0)

Maximum - \frac{4}{3}, \frac{5 ( - \frac{4}{3} ) ^{\frac{4}{5}}}{3}, Minimum (0, 0)

What is the extreme f(x)=x^{4/5}(x+3) ?
The extreme f(x)=x^{4/5}(x+3) is Maximum(-4/3 ,(5(-4/3)^{4/5})/3),Minimum(0,0)