HMMT 二月 2004 · CALC 赛 · 第 6 题
HMMT February 2004 — CALC Round — Problem 6
题目详情
- For x > 0, let f ( x ) = x . Find all values of x for which f ( x ) = f ( x ). 6 2 2
解析
- For x > 0, let f ( x ) = x . Find all values of x for which f ( x ) = f ( x ). Solution: 1 ′ ′ Let g ( x ) = log f ( x ) = x log x . Then f ( x ) /f ( x ) = g ( x ) = 1 + log x . Therefore ′ f ( x ) = f ( x ) when 1 + log x = 1, that is, when x = 1. 6 2 2