题目

若f（x）＝－x＋2ax与g（x）＝a／x+1在区间[1.2]上都是减函数,则a的取值范围是

提问时间：2020-08-07

答案

本题的g(x)题意不清,现分两种情况解答如下：
Case 1：g(x) = 1 + a/x
df/dx = -1 + 2a
let df/dx < 0, we get a < 1/2
dg/dx = -a/x²
let dg/dx < 0, we obtain a > 0
So, ans is 1 ≤ a < 1/2
Case 2 : g(x) = a/(x+1)
df/dx = -1 + 2a
let df/dx < 0, we get a < 1/2
dg/dx = -a/(x+1)²
let dg/dx < 0, we obtain a > 0
So, ans is also 1 ≤ a < 1/2.