讨论函数y=f(x)=x^2,{x<0 x,x≥0},在x=0的可导性
\u8ba8\u8bba\u51fd\u6570f(x)=|x|\u5728x=0\u5904\u7684\u53ef\u5bfc\u60271\u3001\u5f53x>0\u65f6
f(x)=x
f'(x)=1
\u6240\u4ee5f'(0+)=1
\u540c\u7406f'(0-)=-1
x=0\u5904\u5de6\u53f3\u5bfc\u6570\u4e0d\u7b49\uff0c\u4e0d\u53ef\u5bfc\u3002
2\u3001f(0+)=0+1=1
f(0-)=0-1=-1
x=0\u5904\u5de6\u53f3\u6781\u9650\u4e0d\u7b49
\u4e0d\u8fde\u7eed\uff0c\u4e3a\u7b2c\u4e00\u7c7b\u8df3\u8dc3\u95f4\u65ad\u70b9\u3002
\u4f5c\u7528
\u8fde\u7eed\u6027\u7684\u4f5c\u7528\uff1a\u662f\u5bf9\u4e8e\u8fde\u7eed\u73b0\u8c61\u7684\u6570\u5b66\u63cf\u8ff0\uff0c\u53cd\u6620\u4e86\u8fde\u7eed\u73b0\u8c61\u7684\u672c\u8d28\u7279\u70b9\u3002\u8fd9\u662f\u4e00\u79cd\u5bf9\u4e8b\u7269\u53d8\u5316\u8fc7\u7a0b\u7684\u63cf\u8ff0\u3002
\u53ef\u5bfc\u6027\u7684\u4f5c\u7528\uff1a\u662f\u5bf9\u4e8b\u7269\u53d8\u5316\u7387\u7684\u63cf\u8ff0\u3002\u4e5f\u662f\u5bf9\u4e8b\u7269\u53d8\u5316\u8fc7\u7a0b\u7684\u63cf\u8ff0\u3002\u662f\u5728\u8fde\u7eed\u73b0\u8c61\u7684\u57fa\u7840\u4e0a\u624d\u5b58\u5728\u7684\u6027\u8d28\u3002
\u8fde\u7eed\u6027\uff1a\u5de6\u8fde\u7eed\uff1alimx->0-
(-x)=0
\u53f3\u8fde\u7eed\uff1alimx->0+
(x)=0
\u5de6\u8fde\u7eed=\u53f3\u8fde\u7eed
\u6240\u4ee5\u51fd\u6570y\u5728x=0\u51fa\u8fde\u7eed\u3002
\u53ef\u5bfc\u6027\uff1a\u5de6\u5bfc\u6570\uff1alimx->0+
(-x-0)/(x-0)=-1,\u53f3\u5bfc\u6570\uff1alimx->0-
(x-0)/(x-0)=1
\u7531\u4e8e\u5de6\u53f3\u5bfc\u6570\u4e0d\u76f8\u7b49\uff0c\u6240\u4ee5\u51fd\u6570y\u5728x=0\u5904\u4e0d\u53ef\u5bfc\u3002
\u6ce8\u610f\uff1ax-0\u65f6\uff0cy=0\u3002\u540c\u65f6\uff0c\u5728\u56fe\u5f62\u4e0a\u53ef\u4ee5\u770b\u51fax=0\u5904\u662f\u4e00\u4e2a\u6298\u70b9\u3002
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