Question

设函数f(q)=)2sinqcosq+5/2)/(sinq+cosq)Q属于【0,pai/2].的最小值

Answer 1

f(q)=(2sinqcosq+5/2)/(sinq+cosq)

=[(sinq+cosq)²+3/2]/(sinq+cosq)

=(sinq+cosq)+3/[2(sinq+cosq)]

≥2√{(sinq+cosq)×3/[2(sinq+cosq)]}=2√(3/2)=√6 (∵q∈[0,π/2]∴sinq+cosq＞0)

最小值=√6