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

The extreme f(x)=x+3x^{2/3} is Minimum(-8,4),Maximum(0,0)

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

extreme points

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

Minimum (- 8, 4), Maximum (0, 0)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - \frac{1}{8},

Increasing

: - \frac{1}{8} < x < \infty

Plug

x = - 8

into

x + 3 x^{\frac{2}{3}} : 4

Minimum (- 8, 4)

Plug

x = 0

into

x + 3 x^{\frac{2}{3}} : 0

Maximum (0, 0)

Minimum (- 8, 4), Maximum (0, 0)

What is the extreme f(x)=x+3x^{2/3} ?
The extreme f(x)=x+3x^{2/3} is Minimum(-8,4),Maximum(0,0)