HMMT 二月 2002 · CALC 赛 · 第 5 题
HMMT February 2002 — CALC Round — Problem 5
题目详情
- What is the minimum vertical distance between the graphs of 2 + sin( x ) and cos( x )? 2
解析
- What is the minimum vertical distance between the graphs of 2 + sin( x ) and cos( x )? Solution: The derivative of 2 + sin( x ) − cos( x ) is cos x + sin x , which in the interval 3 π 7 π 7 π 0 ≤ x < 2 π is zero at x = , . At , when sin( x ) is negative and cos( x ) is positive, the 4 4 4 √ distance reaches its minimal value of 2 − 2 . 2