切线方程和法线方程 一条直线的切线方程和法线方程有啥关系？
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(2)\u6c42\u5bfc\uff1ay \u2032 = f\u2032(x)\u3002
(3)\u6c42\u51fa\u5728\u70b9x=x0\u5904\u5207\u7ebf\u7684\u659c\u7387k=f \u2032(x0)\u5728\u70b9x=x0\u5904\u6cd5\u7ebf\u659c\u7387 = -1/k = -1/f \u2032(x0)\u3002
(4)\u6839\u636e\u70b9\u659c\u5f0f\uff0c\u5199\u51fa\u5207\u7ebf\u65b9\u7a0b\uff1ay = k(x-x0)+y0 = f \u2032(x0) * { x-x0 } + f(x0)\u5199\u51fa\u5207\u7ebf\u65b9\u7a0b\uff1ay = (-1/k)(x-x0)+y0 ={-1/ f \u2032(x0)} * { x-x0 } + f(x0)\u5982\u679c\u6709\u8981\u6c42\uff0c\u53ef\u6839\u636e\u8981\u6c42\u8fdb\u4e00\u6b65\u5316\u6210\u4e00\u822c\u5f0f\u6216\u659c\u622a\u5f0f\u3002
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\u7528\u5bfc\u6570\u8868\u793a\u66f2\u7ebfy=f(x)\u5728\u70b9M\uff08x0,y0\uff09\u5904\u7684\u5207\u7ebf\u65b9\u7a0b\u4e3a\uff1a y-f(x0)=f'(x0)(x-x0) \u6cd5\u7ebf\u65b9\u7a0b\u4e3a: y-f(x0)=(-1/f'(x0))*(x-x0)\u3002
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y=1/x
y'=-1/x^2
过点(1/2,2)的切线斜率：k=-1/(1/2)^2=-4
切线方程：y-2=-4(x-1/2)
y-2=-4x+2
4x+y-4=0
过(1/2,2)的法线斜率为切线斜率的负倒数：1/4
法线方程：y-2=1/4(x-1/2)
4y-8=x-1/2
8y-16=2x-1
2x-8y+15=0
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绛旓細璇存槑锛歗鈥斺旇〃绀烘鏂 y=1/x y'=-1/x^2 杩囩偣(1/2,2)鐨勫垏绾挎枩鐜囷細k=-1/(1/2)^2=-4 鍒囩嚎鏂圭▼锛歽-2=-4(x-1/2)y-2=-4x+2 4x+y-4=0 杩(1/2,2)鐨勬硶绾挎枩鐜囦负鍒囩嚎鏂滅巼鐨勮礋鍊掓暟锛1/4 娉曠嚎鏂圭▼锛歽-2=1/4(x-1/2)4y-8=x-1/2 8y-16=2x-1 2x-8y+15=0 ...
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绛旓細y'=3^x+x路(3^x)'-2'=3^x+x路3^x路ln3 =3^x路(1+xln3)x=1鏃讹紝y=1 y'=3+3ln3=k鍒 鈭鍒囩嚎鏂圭▼涓 y-1=(3+3ln3)路(x-1)娉曠嚎鏂圭▼涓 y-1=-1/(3+3ln3)路(x-1)
