What is the extreme x^{2/3}-6x^{-1/3} ?

The extreme x^{2/3}-6x^{-1/3} is Minimum(-3,(-3)^{2/3}+2*3^{2/3})

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extreme x^{2/3}-6x^{-1/3}

extreme points

x^{\frac{2}{3}} - 6 x^{- \frac{1}{3}}

Minimum (- 3, (- 3)^{\frac{2}{3}} + 2 \cdot 3^{\frac{2}{3}})

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 3

into

x^{\frac{2}{3}} - 6 x^{- \frac{1}{3}} : (- 3)^{\frac{2}{3}} + 2 \cdot 3^{\frac{2}{3}}

Minimum (- 3, (- 3)^{\frac{2}{3}} + 2 \cdot 3^{\frac{2}{3}})

f (x, y) = \frac{4}{x + y}

f (x) = 3 x^{3} - 36 x + 3

f (x, y) = 1 + 2 x y

f (x, y) = 2 x + y + \frac{2}{x} - \frac{y ^{2}}{2}

What is the extreme x^{2/3}-6x^{-1/3} ?
The extreme x^{2/3}-6x^{-1/3} is Minimum(-3,(-3)^{2/3}+2*3^{2/3})