判断函数增减性时:常有形如“增+增=增,增-减=增”之类形式,还有什么?请帮我总结出来! 用定义判断函数增减性,有什么技巧

\u51fd\u6570\u5355\u8c03\u6027\u7684\u56db\u5219\u8fd0\u7b97\u6cd5\u5219\u662f\u4ec0\u4e48\uff1f\u6bd4\u5982\uff1a\u589e+\u589e=\u589e

\u51fd\u6570\u7684\u5355\u8c03\u6027\u662f\u51fd\u6570\u7684\u91cd\u8981\u6027\u8d28\u4e4b\u4e00,\u5bf9\u4e8e\u5b83\u7684\u8ba8\u8bba\u901a\u5e38\u6709\u5b9a\u4e49\u6cd5\u3001\u56fe\u8c61\u6cd5\u3001\u590d\u5408\u51fd\u6570\u6cd5\u7b49\u3002
\u589e+\u589e=\u589e\uff0c\u51cf+\u51cf=\u51cf\uff0c\u589e-\u51cf=\u589e\uff0c\u51cf-\u589e=\u51cf\uff0c
\u4f8b\u5982\uff1a
\u8bbe\u51fd\u6570y\uff1df\uff08x\uff09\u5728\u4e0a\u9012\u589e,a\u3001b\u4e3a\u5e38\u6570\uff0e
\uff081\uff09\u82e5a\uff1e0,\u5219\u51fd\u6570b\uff0baf\uff08x\uff09\u5728I\u4e0a\u9012\u589e\uff1b
\uff082\uff09\u82e5a\uff1c0,\u5219\u51fd\u6570b\uff0baf\uff08x\uff09\u5728I\u4e0a\u9012\u51cf\uff0e
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\u6269\u5c55\u8d44\u6599\uff1a
\u4e00\u3001\u51fd\u6570\u5355\u8c03\u6027\u7684\u51e0\u4f55\u7279\u5f81\uff1a\u5728\u5355\u8c03\u533a\u95f4\u4e0a\uff0c\u589e\u51fd\u6570\u7684\u56fe\u8c61\u662f\u4e0a\u5347\u7684\uff0c\u51cf\u51fd\u6570\u7684\u56fe\u8c61\u662f\u4e0b\u964d\u7684\u3002
1\u3001\u5f53x1 < x2\u65f6\uff0c\u90fd\u6709f(x1)<f(x2) \u7b49\u4ef7\u4e8e \uff1b
2\u3001\u5f53x1 f(x2) \u3002
3\u3001\u5982\u4e0a\u56fe\u53f3\u6240\u793a\uff0c\u5bf9\u4e8e\u8be5\u7279\u6b8a\u51fd\u6570f(x)\uff0c\u6211\u4eec\u4e0d\u8bf4\u5b83\u662f\u589e\u51fd\u6570\u6216\u51cf\u51fd\u6570\uff0c\u4f46\u6211\u4eec\u53ef\u4ee5\u8bf4\u5b83\u5728\u533a\u95f4 [x1\uff0cx2]\u4e0a\u5177\u6709\u5355\u8c03\u6027\u3002
\u4e8c\u3001\u8fd0\u7b97\u6027\u8d28
1\u3001f(x)\u4e0ef(x)+a\u5177\u6709\u76f8\u540c\u5355\u8c03\u6027\uff1bf(x)\u4e0e g(x) = a\u00b7f(x)\u5728 a>0 \u65f6\u6709\u76f8\u540c\u5355\u8c03\u6027\uff0c\u5f53 a<0 \u65f6\uff0c\u5177\u6709\u76f8\u53cd\u5355\u8c03\u6027\uff1b
2\u3001\u5f53f(x)\u3001g(x)\u90fd\u662f\u589e\uff08\u51cf\uff09\u51fd\u6570\u65f6\uff0c\u82e5\u4e24\u8005\u90fd\u6052\u5927\u4e8e\u96f6\uff0c\u5219f(x)\u00d7g(x)\u4e3a\u589e\uff08\u51cf\uff09\u51fd\u6570\uff1b\u82e5\u4e24\u8005\u90fd\u6052\u5c0f\u4e8e\u96f6\uff0c\u5219\u4e3a\u51cf\uff08\u589e\uff09\u51fd\u6570\uff1b
3\u3001\u4e24\u4e2a\u589e\u51fd\u6570\u4e4b\u548c\u4ecd\u4e3a\u589e\u51fd\u6570\uff1b\u589e\u51fd\u6570\u51cf\u53bb\u51cf\u51fd\u6570\u4e3a\u589e\u51fd\u6570\uff1b\u4e24\u4e2a\u51cf\u51fd\u6570\u4e4b\u548c\u4ecd\u4e3a\u51cf\u51fd\u6570\uff1b\u51cf\u51fd\u6570\u51cf\u53bb\u589e\u51fd\u6570\u4e3a\u51cf\u51fd\u6570\uff1b\u51fd\u6570\u503c\u5728\u533a\u95f4\u5185\u540c\u53f7\u65f6\uff0c \u589e\uff08\u51cf\uff09\u51fd\u6570\u7684\u5012\u6570\u4e3a\u51cf\uff08\u589e\uff09\u51fd\u6570\u3002
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1\u2014\u5355\u8c03\u6027

\u3000\u30001.\u5355\u8c03\u6027\u7684\u5b9a\u4e49\uff1a
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\u3000\u30002\u3001\u5982\u679c\u51fd\u6570y=f\uff08x\uff09\u5728\u533a\u95f4\u4e0a\u662f\u589e\u51fd\u6570\u6216\u51cf\u51fd\u6570\uff0c\u5c31\u8bf4\u51fd\u6570y=f\uff08x\uff09\u5728\u533a\u95f4D\u4e0a\u5177\u6709\uff08\u4e25\u683c\u7684\uff09\u5355\u8c03\u6027\uff0c\u533a\u95f4D\u79f0\u4e3a\u51fd\u6570f\uff08x\uff09\u7684\u5355\u8c03\u533a\u95f4\u3002\u5982\u679c\u51fd\u6570y=f\uff08x\uff09\u5728\u533a\u95f4D\u4e0a\u662f\u589e\u51fd\u6570\u6216\u51cf\u51fd\u6570\uff0c\u533a\u95f4D\u79f0\u4e3a\u51fd\u6570f\uff08x\uff09\u7684\u5355\u8c03\u589e\u6216\u51cf\u533a\u95f4
\u3000\u30003\u3001\u6700\u503c\u7684\u5b9a\u4e49\uff1a
\u3000\u3000\u6700\u5927\u503c\uff1a\u4e00\u822c\u5730\uff0c\u8bbe\u51fd\u6570y\uff1df\uff08x\uff09\u7684\u5b9a\u4e49\u57df\u4e3aI\uff0c\u5982\u679c\u5b58\u5728\u5b9e\u6570M\uff0c\u6ee1\u8db3\uff1a \u2460\u5bf9\u4e8e\u4efb\u610f\u7684x\u2208I\uff0c\u90fd\u6709f\uff08x\uff09\u2264M\uff1b\u2461\u5b58\u5728x0\u2208I\uff0c\u4f7f\u5f97f\uff08x0\uff09\uff1dM\uff1b\u90a3\u4e48\uff0c\u79f0M\u662ff\uff08x\uff09\u7684\u6700\u5927\u503c\uff0e
\u3000\u3000\u6700\u5c0f\u503c\uff1a\u4e00\u822c\u5730\uff0c\u8bbe\u51fd\u6570y\uff1df\uff08x\uff09\u7684\u5b9a\u4e49\u57df\u4e3aI\uff0c\u5982\u679c\u5b58\u5728\u5b9e\u6570M\uff0c\u6ee1\u8db3\uff1a \u2460\u5bf9\u4e8e\u4efb\u610f\u7684x\u2208I\uff0c\u90fd\u6709f\uff08x\uff09\u2265M\uff1b\u2461\u5b58\u5728x0\u2208I\uff0c\u4f7f\u5f97f\uff08x0\uff09\uff1dM\uff1b\u90a3\u4e48\uff0c\u79f0M\u662ff\uff08x\uff09\u7684\u6700\u5c0f\u503c
\u3000\u3000\u5224\u65ad\u51fd\u6570f\uff08x\uff09\u5728\u533a\u95f4D\u4e0a\u7684\u5355\u8c03\u6027\u7684\u65b9\u6cd5\uff1a
\u3000\u3000\uff081\uff09\u5b9a\u4e49\u6cd5\uff1a\u5176\u6b65\u9aa4\u662f\uff1a
\u3000\u3000\u2460\u4efb\u53d6x1\uff0cx2\u2208D\uff0c\u4e14x1\uff1cx2\uff1b
\u3000\u3000\u2461\u4f5c\u5deef\uff08x1\uff09-f\uff08x2\uff09\u6216\u4f5c\u5546 \uff0c\u5e76\u53d8\u5f62\uff1b
\u3000\u3000\u2462\u5224\u5b9af\uff08x1\uff09-f\uff08x2\uff09\u7684\u7b26\u53f7\uff0c\u6216\u6bd4\u8f83 \u4e0e1\u7684\u5927\u5c0f\uff1b
\u3000\u3000\u2463\u6839\u636e\u5b9a\u4e49\u4f5c\u51fa\u7ed3\u8bba\u3002
\u3000\u3000\uff082\uff09\u590d\u5408\u6cd5\uff1a\u5229\u7528\u57fa\u672c\u51fd\u6570\u7684\u5355\u8c03\u6027\u7684\u590d\u5408\u3002
\u3000\u3000\uff083\uff09\u56fe\u8c61\u6cd5\uff1a\u5373\u89c2\u5bdf\u51fd\u6570\u5728\u533a\u95f4D\u4e0a\u90e8\u5206\u7684\u56fe\u8c61\u4ece\u5de6\u5f80\u53f3\u770b\u662f\u4e0a\u5347\u7684\u8fd8\u662f\u4e0b\u964d\u7684\u3002

复合函数:f[g(x)],同增异减
f(x)*g(x),不一定,要求导算一算,例如x*x,都为增函数,但是相乘以后就分区间为增或减函数
增+增=增,增-减=增,减+减=减

减+减=减 减-增=减
还有增-增和减-减是不能判断的

这是复合函数当中判断增减性的性质

判断复合函数的单调性的步骤如下:

(1)
求复合函数定义域;
(2)
将复合函数分解为若干个常见函数(一次、二次、幂、指数、对数函数);
(3)
判断每个常见函数的单调性;
(4)
将复合函数的定义域分段(每个常见函数在每段定义域上具有单调性);
(5)
根据“通增异减”求出复合函数的单调性。

复合函数,同增异减。其他的要看情况

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