Question

求函数f(x)=x/x2+3(x∈[√2/2,3√2])的最小值?

Answer 1

x∈[√2/2,3√2],
依基本不等式得
f(x)＝x/(x^2+3)
≤x/(2√3x)
＝√3/6.
x^2＝3,即x＝√3时,
f(x)|max＝√3/6.
同时,
f(x)|min＝min{f(√2/2),f(√3/6),f(3√2)}
＝f(3√2)或f(√2/2)
＝√2/7.