What is the extreme x+3/2 x^{2/3} ?

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

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extreme x+3/2 x^{2/3}

extreme points

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

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

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < \infty

Plug

x = - 1

into

x + \frac{3}{2} x^{\frac{2}{3}} : \frac{1}{2}

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

Plug

x = 0

into

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

Maximum (0, 0)

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

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