Question

1.函数y=7-4sinxcosx+4 cos^2x-4cos^4x,求最大与最小值.2.f(x)=2cos^2wx+2

Answer 1

1、y=7-4sinxcosx+4 cos^2x-4cos^4x=7-4sinxcosx+4cosx^2(1-cosx^2)

=7-4sinxcosx+4sinx^2cosx^2=(2sinxcosx-1)^2+6

=(sin2x-1)^2+6

∴ymax=(-1-1)^2+6=10

ymin=(1-1)^2+6=6

2、f(x)=2cos^2wx+2sinwx*coswx+1=1+cos2wx+sin2wx+1

=√2sin(2wx+π/4)+2

函数最小正周期T=2π/2w=π/2

∴w=2

f(x)max=√2+2,此时4x+π/4=2kπ+π/2,即x=kπ/2+π/16

∴X={x|x=kπ/2+π/16,k∈Z}