Question

Tìm GTLN, GTNN:

a, \(y=4-3\cos2x\).

b, \(y=sin^2x+3\).

c, \(y=2\sin x\cos x+3\).

Answer 1

a: -1<=cos2x<=1

=>3>=-3cos2x>=-3

=>7>=-3cos2x+4>=1

=>7>=y>=1

\(y_{min}=1\) khi \(cos2x=1\)

=>2x=k2pi

=>x=kpi

\(y_{max}=-1\) khi cos2x=-1

=>2x=pi+k2pi

=>x=pi/2+kpi

b: \(0< =sin^2x< =1\)

=>\(3< =sin^2x+3< =4\)

=>3<=y<=4

y min=3 khi sin^2x=0

=>sinx=0

=>x=kpi

y max=4 khi sin^2x=1

=>cos^2x=0

=>x=pi/2+kpi

c: \(y=sin2x+3\)

-1<=sin2x<=1

=>-1+3<=sin2x+3<=1+3

=>2<=y<=4

\(y_{min}=2\) khi sin 2x=-1

=>2x=-pi/2+k2pi

=>x=-pi/4+kpi

y max=4 khi sin2x=1

=>2x=pi/2+k2pi

=>x=pi/4+kpi