Question

已知f(x)=a(2cos平方x/2+sinx)+b (1)当a=1,f(x)的单调区间.(2)当x属于［0,派］,f(

Answer 1

f(x)=a(2cos平方x/2+sinx)+b=a(cosx+sinx+1)+b=a根号2sin(x+π/4)+a+b

(1）当a=1时,f(x)在【2kπ-3π/4,2kπ+π/4]k属于z,上是增函数,在【2kπ+π/4,2kπ+5π/4]k属于z,是减函数

(2)当x属于［0,派］,f(x)值域［3,4］可知,a（根号2+1）+b=4,-a+b=3,解得a=1-二分之根号2