求最值1、y=5+根号2x^2-10x+3 2、y=(x-1)/(x+2) x属于[-1,3]
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求最值1、y=5+根号2x^2-10x+3 2、y=(x-1)/(x+2) x属于[-1,3]
![求最值1、y=5+根号2x^2-10x+3 2、y=(x-1)/(x+2) x属于[-1,3]](/uploads/image/z/16878491-35-1.jpg?t=%E6%B1%82%E6%9C%80%E5%80%BC1%E3%80%81y%3D5%2B%E6%A0%B9%E5%8F%B72x%5E2-10x%2B3+2%E3%80%81y%3D%28x-1%29%2F%28x%2B2%29+x%E5%B1%9E%E4%BA%8E%5B-1%2C3%5D)
∵根号(2x^2-10x+3)=根号[2(x-2.5)^2-9.5]≥0
y=5+根号(2x^2-10x+3)≥5,最小值5
y=(x-1)/(x+2) =(x+2-3)/(x+2)=1 - 3/(x+2)
x+2单调增
3/(x+2)单调减
1 - 3/(x+2)单调增
y=(x-1)/(x+2)=1 - 3/(x+2)单调增
x=-1时,最小值1-3/(-1+2)=-2
x=3时,最大值1-3/(3+2)=2/5
y=5+根号(2x^2-10x+3)≥5,最小值5
y=(x-1)/(x+2) =(x+2-3)/(x+2)=1 - 3/(x+2)
x+2单调增
3/(x+2)单调减
1 - 3/(x+2)单调增
y=(x-1)/(x+2)=1 - 3/(x+2)单调增
x=-1时,最小值1-3/(-1+2)=-2
x=3时,最大值1-3/(3+2)=2/5
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