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Home » \[ 120 - 1.5t = 0 \] - Sterling Industries

\[ 120 - 1.5t = 0 \] - Sterling Industries

📅 April 15, 2026 👤 scraface

Apr 15, 2026

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📌 f(x) = 4\left(\left(x + \frac{3}{2}\right)^2 - \frac{9}{4}\right) + 9 = 4\left(x + \frac{3}{2}\right)^2 - 9 + 9 = 4\left(x + \frac{3}{2}\right)^2

📌 項 \(4\left(x + \frac{3}{2}\right)^2\) は常に非負であり、\(\left(x + \frac{3}{2}\right)^2 = 0\) のときに最小値 0 を取ります。これは \(x = -\frac{3}{2}\) のときに起こります。

📌 \(x = -\frac{3}{2}\) を元の関数に代入します:

📌 f\left(-\frac{3}{2}\right) = 4\left(-\frac{3}{2} + \frac{3}{2}\right)^2 = 4 \cdot 0 = 0

📌 したがって、関数 \(f(x) = 4x^2 + 12x + 9\) の最小値は \(\boxed{0}\) です。

📌 問題: \(\left(\cos x + \sec x\right)^2 + \left(\sin x + \csc x\right)^2\) の最小値を求めよ。

📌 \cos x + \sec x = \cos x + \frac{1}{\cos x}, \quad \sin x + \csc x = \sin x + \frac{1}{\sin x}

📌 \left(\cos x + \frac{1}{\cos x}\right)^2 + \left(\sin x + \frac{1}{\sin x}\right)^2

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