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6Â¥: Originally posted by Àî¸ÉÊÇ at 2015-09-14 08:40:04
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Let c be one maximum point. The area of triangle (a,b,f(c)) is not more than the integral of f in (a,b).

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ÓÉÓÚf(x)¶þ½×¿Éµ¼ÇҺ㲻´óÓÚÁ㣬Òò´Ë f(x)ÔÚ[a,b]Ò»¶¨´æÔÚ×î´óÖµM¡¢×îСֵmÒÔ¼°Æ½¾ùÖµp=Integral{f(x)*dx,a,b}¡£²¢ÇÒÈ¡µÃƽ¾ùÖµµÄλÖõãÖÁÉÙÓÐÁ½¸ö¡£¼ÙÉèx=qÊÇÓëÈ¡µÃ×îСֵµÄµãx=rÏàÁÚµÄȡƽ¾ùÖµµÄµã£¬ÔòÔÚqÓërÖ®¼ä±ØÈ»´æÔÚÒ»µãc£¬Ê¹µÃf(c)СÓÚÆ½¾ùÖµp,¸ü²»ÒªËµÊÇСÓÚÆ½¾ùÖµµÄÁ½±¶ÁË¡£

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