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HMMT 二月 2008 · CALC 赛 · 第 2 题

HMMT February 2008 — CALC Round — Problem 2

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 3 ] Let ` be the line through (0 , 0) and tangent to the curve y = x + x + 16. Find the slope of ` . ∫ y 1
解析
  1. [ 3 ] Let ` be the line through (0 , 0) and tangent to the curve y = x + x + 16. Find the slope of ` . 3 3 Answer: 13 Let the point of tangency be ( t, t + t + 16), then the slope of is ( t + t + 16) /t . On 2 2 the other hand, since dy/dx = 3 x + 1, the slope of is 3 t + 1. Therefore, 3 t + t + 16 2 = 3 t + 1 . t 3 2 Simplifying, we get t = 8, so t = 2. It follows that the slope is 3(2) + 1 = 13. ∫ y 1