What is the extreme f(x)=(1+x/5)x^{2/3} ?

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

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extreme f(x)=(1+x/5)x^{2/3}

extreme points

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

Maximum (- 2, \frac{3 ( - 2 ) ^{\frac{2}{3}}}{5}), Minimum (0, 0)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 2

into

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

Maximum (- 2, \frac{3 ( - 2 ) ^{\frac{2}{3}}}{5})

Plug

x = 0

into

(1 + \frac{x}{5}) x^{\frac{2}{3}} : 0

Minimum (0, 0)

Maximum (- 2, \frac{3 ( - 2 ) ^{\frac{2}{3}}}{5}), Minimum (0, 0)

3 x + y

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

f (x) = - x^{2} + 190

f (x) = 28 x - \frac{x ^{2}}{105}

3^{x - 1}

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