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
问题描述:
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
答
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 dg/dx = -a/x²
let dg/dx 0
So, ans is 1 ≤ a Case 2 : g(x) = a/(x+1)
df/dx = -1 + 2a
let df/dx dg/dx = -a/(x+1)²
let dg/dx 0
So, ans is also 1 ≤ a