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Home » Work Smarter, Not Harder: Split First & Last Names in Excel Instantly! - RTA

Work Smarter, Not Harder: Split First & Last Names in Excel Instantly! - RTA

📅 May 9, 2026 👤 scraface

May 09, 2026

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📌 A linguist studying the evolution of language is analyzing the frequency of certain phonetic shifts in historical texts. If the frequency of a phonetic shift in a text is modeled by \( f(x) = rac{2x + 3}{x - 1} \), find the value of \( x \) that maximizes \( f(x) \).

📌 To maximize the function \( f(x) = rac{2x + 3}{x - 1} \), we first find its derivative to locate critical points. Using the quotient rule:

📌 f'(x) = rac{(x - 1)(2) - (2x + 3)(1)}{(x - 1)^2} = rac{2x - 2 - 2x - 3}{(x - 1)^2} = rac{-5}{(x - 1)^2}

📌 The derivative \( f'(x) = rac{-5}{(x - 1)^2} \) is always negative for all \( x

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