题目

若f(x)=(1-λ)sinx-(1/2+1/2λ)cosx+1在[-π/2,π/2]是增函数,求λ取值范围!

提问时间：2021-01-02

答案

若f(x)=(1-λ)sinx-(1/2+1/2λ)cosx+1在[-π/2,π/2]是增函数,求λ取值范围!
解析：设cosθ=(1-λ)/√[5/4+5λ^2/4-3λ/2],sinθ=(1/2+1/2λ)/√[5/4+5λ^2/4-3λ/2]
∴f(x)=√[5/4+5λ^2/4-3λ/2]sin(x-θ)+1
要使f(x)在[-π/2,π/2]是增函数,须使θ=0
令1/2+1/2λ=0==>λ=-1
∴f(x)在[-π/2,π/2]是增函数,λ=-1