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HMMT 十一月 2010 · 冲刺赛 · 第 4 题

HMMT November 2010 — Guts Round — Problem 4

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 6 ] Let x be a real number. Find the maximum value of 2 .
解析
  1. [ 6 ] Let x be a real number. Find the maximum value of 2 . √ 4 y y Answer: 2 Consider the function 2 . This is monotonically increasing, so to maximize 2 , you 2 simply want to maximize y . Here, y = x (1 − x ) = − x + x is a parabola opening downwards. The vertex of the parabola occurs at x = ( − 1) / ( − 2) = 1 / 2, so the maximum value of the function is √ 4 (1 / 2)(1 / 2) 2 = 2.