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Home » Now substitute into $ f(x) $: - Coaching Toolbox

Now substitute into $ f(x) $: - Coaching Toolbox

📅 May 3, 2026 👤 scraface

May 03, 2026

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We minimize this expression for $ s \in (\sqrt{2}, \sqrt{2}] $, since...
f(s) = \left( \frac{2s}{s^2 - 1} \right)^2
We minimize $ f(s) $ on $ (1, \sqrt{2}) $.
Let’s test $ s = \sqrt{2} $:
f(\sqrt{2}) = \left( \frac{2\sqrt{2}}{2 - 1} \right)^2 = (2\sqrt{2})^2...
Now check derivative or behavior: as $ s \to 1^+ $, $ f(s) \to \infty...
\min (\sec x + \csc x)^2 = 8
Question: A science policy analyst is modeling the efficiency of a new...
Find the minimum value of this expression for $ x \in (0, \frac{\pi}{2...
We expand both terms:

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