若实数x，y满足等式(x-2)²+y²=3,那么y/x的最大值为多少？
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u= y/x
u^2
= y^2/x^2
=[3-(x-2)^2]/x^2
=( -x^2 +4x -1 )/x^2
=-1 + 4/x - 1/x^2
d/dx (u^2)
= -4/x^2 + 2/x^3
d/dx (u^2) =0
-4/x^2 + 2/x^3 =0
-4x+2=0
x=1/2
(u^2)'' =8/x^3 - 6/x^4
(u^2)''| x=1/2
=64 -96
<0
max
max u^2
=-1 + 4(2) - 4
=-1+8 -4
=3
max u = max (y/x) = √3
u^2
= y^2/x^2
=[3-(x-2)^2]/x^2
=( -x^2 +4x -1 )/x^2
=-1 + 4/x - 1/x^2
d/dx (u^2)
= -4/x^2 + 2/x^3
d/dx (u^2) =0
-4/x^2 + 2/x^3 =0
-4x+2=0
x=1/2
(u^2)'' =8/x^3 - 6/x^4
(u^2)''| x=1/2
=64 -96
<0
max
max u^2
=-1 + 4(2) - 4
=-1+8 -4
=3
max u = max (y/x) = √3
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