常用的基本不等式和重要的不等式

、常用的基本不等式和重要的不等式：（1）0,0,2aaRa当且仅当”取“,0a（2）abbaRba2,,22则（3）Rba,，则abba2（4）222)2(2baba（5）2211222babaabba4、最值定理:设xyyxyx2,0,由（1）如积PyxPxy2(有最小值定值），则积（2）如积22(）有最大值（定值），则积SxySyx即:积定和最小，和定积最大新疆源头学子小屋特级教师王新敞@[e-mail]王新敞特级教师源头学子小屋新疆运用最值定理求最值的三要素：一正二定三相等5、解不等式关键在于等价转化：(1)f(x)g(x)0f(x)0g(x)0f(x)0g(x)0·＞与＞＞或＜＜同解．(2)f(x)g(x)0f(x)0g(x)0f(x)0g(x)0·＜与＞＜或＜＞同解．(3)f(x)g(x)0f(x)0g(x)0f(x)0g(x)0(g(x)0)＞与＞＞或＜＜同解．≠(4)f(x)g(x)0f(x)0g(x)0f(x)0g(x)0(g(x)0)＜与＞＜或＜＞同解．≠(5)|f(x)|＜g(x)与－g(x)＜f(x)＜g(x)同解．(g(x)＞0)(6)|f(x)|＞g(x)与①f(x)＞g(x)或f(x)＜－g(x)(其中g(x)≥0)；②g(x)＜0同解(7)f(x)g(x)f(x)[g(x)]f(x)0g(x)0f(x)0g(x)02＞与＞≥≥或≥＜同解．(8)f(x)g(x)f(x)[g(x)]f(x)02＜与＜≥同解．(9)当a＞1时，af(x)＞ag(x)与f(x)＞g(x)同解，当0＜a＜1时，af(x)＞ag(x)与f(x)＜g(x)同解．(10)a1logf(x)logg(x)f(x)g(x)f(x)0aa当＞时，＞与＞＞同解．当＜＜时，＞与＜＞＞同解．0a1logf(x)logg(x)f(x)g(x)f(x)0g(x)0aa一、例题精讲：