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

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

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

extreme points

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

Maximum (- 2, - 2^{\frac{1}{3}} - \frac{1}{( - 2 ) ^{\frac{2}{3}}})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 2

into

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

Maximum (- 2, - 2^{\frac{1}{3}} - \frac{1}{( - 2 ) ^{\frac{2}{3}}})

f (x) = x^{4} - 2 x^{3} - 11 x^{2} + 12 x + 36

y = 9 x^{3} - 7

x^{3} - 12 x^{2} + 45 x + 8

x^{4} - 4 x^{2} - 2, - 2 \leq x \leq 2

f (x, y) = \frac{y ^{2} - x}{x ^{2} + 1}

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