Question

用均值定理证明x>0时2-3x-(4/x)最大值是2-4√3

Answer 1

2-3x-(4/x)=2-(3x+(4/x)),

由均值定理得3x+(4/x)≥2√(3x*(4/x))=2√12=4√3,该式当3x=4/x时取等号,

故2-3x-(4/x)≤4-2√3,

当3x=4/x,即x=2√3/3时,上式取等号,故2-3x-(4/x)最大值是2-4√3.