fx=sinx+cosx
=√2(√2/2*sinx+√2/2*cosx)
=√2sin(x+π/4)
∵x∈〔0,π〕
∴当x+π/4=π/2即x=π/4时,sin(x+π/4)=1取得最大值
于是原函数的最大值为√2