求法线方程 求以下法线方程
\u6cd5\u7ebf\u65b9\u7a0b\u600e\u4e48\u6c42\u89e3\u9898\u8fc7\u7a0b\u5982\u4e0b\uff1a
\u6cd5\u7ebf\u65b9\u7a0b\uff1ay-f(x0)=-1/f\u2018(x0)*[x-x0]
\u56e0\u4e3ay=x^2\u4e0a\u7684\u5207\u70b9\u4e3a\uff081,1\uff09
\u6240\u4ee5y-1=-1/2(x-1)
\u6574\u7406\u5f97\uff0cy=-1/2x+3/2
\u6269\u5c55\u8d44\u6599\uff1a
\u6cd5\u7ebf\u659c\u7387\u4e0e\u5207\u7ebf\u659c\u7387\u4e58\u79ef\u4e3a-1\uff0c\u5373\u82e5\u6cd5\u7ebf\u659c\u7387\u548c\u5207\u7ebf\u659c\u7387\u5206\u522b\u7528\u03b1\u3001\u03b2\u8868\u793a\uff0c\u5219\u5fc5\u6709\u03b1*\u03b2=-1\u3002\u6cd5\u7ebf\u53ef\u4ee5\u7528\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u6765\u8868\u793a\uff0c\u5373\u6cd5\u7ebf\u65b9\u7a0b\u3002\u4e0e\u5bfc\u6570\u6709\u76f4\u63a5\u7684\u8f6c\u6362\u5173\u7cfb\u3002
\u66f2\u7ebf\u5728\u70b9\uff08x0\uff0cy0\uff09\u7684\u6cd5\u7ebf\u65b9\u7a0b
,
\u5148\u6c42\u51fd\u6570\u7684\u4e00\u9636\u5bfc\u6570\uff0cy\u2018=2x\uff0c
\u4ee3\u5165\u8be5\u70b9\u5904\u7684\u6a2a\u5750\u6807\u5f97y'(1)=2\uff0c
\u8fd9\u662f\u8be5\u70b9\u5904\u5207\u7ebf\u7684\u659c\u7387\uff0c\u800c\u6cd5\u7ebf\u548c\u5207\u7ebf\u5782\u76f4\uff0c
\u6240\u4ee5\u6cd5\u7ebf\u7684\u659c\u7387\u4e3a-1/2\uff0c\u901a\u8fc7\u70b9\u659c\u5f0f\u5f97\u6cd5\u7ebf\uff1a
y=-(x-1)/2+1=-x/2+3/2\u3002
代入该点处的横坐标得y'(1)=2，
这是该点处切线的斜率，而法线和切线垂直，
所以法线的斜率为-1/2，通过点斜式得法线：
y=-(x-1)/2+1=-x/2+3/2。
y'=2x
所以，在(1,1)处的切线斜率为2，法线斜率=-1/2
所以，法线方程为：y=(-1/2)(x-1)+1，即：y=-x/2 +3/2
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