Question

已知函数f(x)=cosx-cos(x+π*2),x∈R （1）求f(x)的最大值 （2）若f(α

Answer 1

f(x)=cosx-cos(x+π/2)

=-2(sin(x+x+π/2)/2sin(x-x-π/2)/2

=-2(sin(x+π/4)sin(-π/4)

=√2sin(x+π/4)

所以最大值是√2,最小值是-√2

增区间 2kπ+π/2>=x+π/4>=2kπ-π/2

2kπ+π4>=x>=2kπ-3π/4区间为增区间

减区间 2kπ+3π/2>=x+π/4>=2kπ+π/2

2kπ+5π/4>=x>=2kπ+π/4区间为减区间

如果帮到您的话,(右上角采纳)