Question

设函数f(x)=2cos²x+2√3sinxcosx+m(x∈R)

Answer 1

解:

f(x)

=1+cos2x+√3sin2x+m

=2sin(2x+π/6)+1+m

∴T=π,

x∈[0,π/2]时,

2x+π/6∈[π/6,7π/6],

f(x)∈[m+1,m+3],

值域宽度是2,不可能是[1/2,7/2],

即永远不可能是[1/2,7/2]