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Home » Now subtract Eq 1 from Eq 2: - Belip

Now subtract Eq 1 from Eq 2: - Belip

📅 May 6, 2026 👤 scraface

May 06, 2026

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📌 h(y) = 2y + \frac{1}{2y}

📌 Using the AM-GM inequality:

📌 2y + \frac{1}{2y} \geq 2\sqrt{2y \cdot \frac{1}{2y}} = 2

📌 Equality holds when $ 2y = \frac{1}{2y} \Rightarrow 4y^2 = 1 \Rightarrow y = \frac{1}{2} $.

📌 g(x) = h(y) + 2 = 2 + 2 = 4

📌 Therefore, the minimum value of $ g(x) $ is:

📌 Question: A materials scientist is analyzing the stiffness of a composite material, modeled by the expression

📌 Find the minimum value of this expression for $ x \in \left(0, \frac{\pi}{2}\right) $.

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