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222-9+11+12:2*14+14 = ? ( )

Toán Lớp 11: tìm min max hàm số sau y=21/5-2sin^2x+3cos2x y=2-4 căn(3+4sin3xcos3x)

Toán Lớp 11: tìm min max hàm số sau
y=21/5-2sin^2x+3cos2x
y=2-4 căn(3+4sin3xcos3x)

Comments ( 1 )

  1. y=21/5 -2sin^2x+3cos2x=21/5-(1-cos2x)+3cos2x=16/5+4cos2x
    -1 <= cos2x<=1
    <=> -4<=4cos2x<=4
    <=>-4/5 <= 16/5+4cos2x<=36/5
    => y_(min)=-4/5 ; y_(max)=36/5
    .
    y=2-4\sqrt(3+4sin3xcos3x)=2-4\sqrt(3+2sin6x)
    -1 <= sin6x <=1
    <=>1<=3+2sin6x <=5
    <=>1<=\sqrt(3+2sin6x) <=\sqrt5
    <=>-2>= 2-4\sqrt(3+2sin6x) >= -4\sqrt5+2
    => y_(min)=-4\sqrt5+2 ; y_(max)=-2

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222-9+11+12:2*14+14 = ? ( )