函数fx=sinx+cosx=√2sin(x+π/4)
∵x∈[-π/2,π/2]
∴x+π/4∈[-π/4,3π/4]
=>-√2/2≤sin(x+π/4)≤1
=>-1≤y=√2sin(x+π/4)≤√2这个。。。第一步我就不知道为什么。。。sinx+cosx=√2(√2/2sinx+√2/2cosx)=√2(sinxcosπ/4+cosxsinπ/4)=√2sin(x+π/4)好吧，如果用导数怎么做呀？麻烦告诉我一下f'(x)=cosx-sinx=0=>cosx=sinx=>tanx=1=>x=π/4为极大值点。则f(π/4)=sinπ/4+cosπ/4=√2f(-π/2)=f(π/2)=比较大小就可以了。内个，为什么四分之派的时候是极大值呀，怎么确定是极大的？画图么？画图的话怎么画？。。。谢谢解答！！x<π/4,f'(x)=cosx-sinx>0f(x)为增函数x>π/4,f'(x)=cosx-sinx<0f(x)为减函数=>x=π/4为极大值点