HMMT 二月 2008 · CALC 赛 · 第 2 题

英文解析

2. [ 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,
   t + t + 163 = 3 t + 1 .2
   3 2 t
   Simplifying, we get t = 8, so t = 2. It follows that the slope is 3(2) + 1 = 13.
   ∫
   1 y