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high point university north carolina tuition - NBX Soluciones

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 \(x = -\frac{1}{5}\) を \(y = 2x + 3\) に代入します:

📌 y = 2\left(-\frac{1}{5}\right) + 3 = -\frac{2}{5} + 3 = \frac{13}{5}

📌 したがって、直線 \(y = 2x + 3\) 上の点 \((1, 2)\) に最も近い点は \(\left(-\frac{1}{5}, \frac{13}{5}\right)\) です。答えは \(\boxed{\left(-\frac{1}{5}, \frac{13}{5}\right)}\) です。

📌 問題: 関数 \(f(x) = 4x^2 + 12x + 9\) の最小値を求めよ。

📌 解: 関数 \(f(x) = 4x^2 + 12x + 9\) の最小値を見つけるために、まず平方完成を行います。この関数は上に開く二次式です（\(x^2\) の係数が正であるため）。

📌 f(x) = 4x^2 + 12x + 9 = 4(x^2 + 3x) + 9

📌 \(x\) の係数の半分を 2 乗したものを加算および減算します:

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

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