What is the extreme 2/(x^{12)}-1/(x^6) ?

The extreme 2/(x^{12)}-1/(x^6) is Minimum(-\sqrt[3]{2},-1/8),Minimum(\sqrt[3]{2},-1/8)

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extreme 2/(x^{12)}-1/(x^6)

extreme points

\frac{2}{x ^{12}} - \frac{1}{x ^{6}}

Solution steps

Find the critical points:

Domain of

\frac{2}{x ^{12}} - \frac{1}{x ^{6}} : x < 0 or x > 0

Find intervals:

Decreasing

Increasing

Decreasing

Increasing

Plug the extreme point

into

\frac{2}{x ^{12}} - \frac{1}{x ^{6}} \Rightarrow y = - \frac{1}{8}

Plug the extreme point

into

\frac{2}{x ^{12}} - \frac{1}{x ^{6}} \Rightarrow y = - \frac{1}{8}

f (x) = \frac{x ^{2} - 4}{x - 1}

f (x, y) = 2 x - 5 y + 3

f (x, y) = 2 x^{2} - 5 x y + 3 y^{4} + 5

f (x, y) = 2 x y

f (x) = x^{2} (x - 1) (x + 2)

What is the extreme 2/(x^{12)}-1/(x^6) ?
The extreme 2/(x^{12)}-1/(x^6) is Minimum(-\sqrt[3]{2},-1/8),Minimum(\sqrt[3]{2},-1/8)