若實數x,y滿足-4 ≤ x ≤ -3,1 ≤ y ≤ 3,試求下列各式的範圍 (1)3x+2y (2)3x-2y (3)xy (4)x^2+y^2?

Sol
－4<=x<－3，1<=y<=3
(1) 3x+2y
－12<=3x<－9，2<=2y<=6
－12+2<=3x+2y<=－9+6
－10<=3x+2y<=－3
(2) 3x－2y
－3<=－y<=－1
－6<=－2y<=－2
－12－6<=3x－2y<=－9－2
－18<=3x－2y<=－11
(3) xy
(－4)*1=－4
(－4)*3=－12
(－3)*1=－3
(－3)*3=－9
Max(－4，－12，－3，－9)=－3
Min(－4，－12，－3，－9)=－12
－12<=xy<=－3
(4) x^2+y^2
－4<=x<=－3
9<=x^2<=16
1<=y<=3
1<=y^2<=9
9+1<=x^2+y^2<=16+9
10<=x^2+y^2>=25

1)
-4 ≤ x ≤ -3
-12 ≤ 3x ≤ -9
1 ≤ y ≤ 3
2 ≤ 2y ≤ 6
-10 ≤ 3x+2y ≤-3

2)
-14 ≤ 3x-2y ≤ -15

3)
-9 ≤ xy ≤ -4

4)
-4 ≤ x ≤ -3
9 ≤ x^2 ≤ 16
1 ≤ y ≤ 3
1 ≤ y^2 ≤ 9
10 ≤ x^2+y^2 ≤ 15