What's the minimum of if ?
Let's try this
If then you can set where
Then
And
\cosh^{10}(\alpha) + \sinh^{10}(\alpha))" alt="K'(\alpha) = 12 \cosh(\alpha) \:\sinh(\alpha)\\cosh^{10}(\alpha) + \sinh^{10}(\alpha))" />
Therefore
And K(x) is increasing over
If then you can set where
Then
And
\cosh^{10}(\alpha) + \sinh^{10}(\alpha))" alt="K'(\alpha) = 12 \cosh(\alpha) \:\sinh(\alpha)\\cosh^{10}(\alpha) + \sinh^{10}(\alpha))" />
Therefore
And K(x) is decreasing over
If then you can set where
Then
And
\sin^{10}(\alpha) - \cos^{10}(\alpha))" alt="K'(\alpha) = 12 \cos(\alpha) \:\sin(\alpha)\\sin^{10}(\alpha) - \cos^{10}(\alpha))" />