新高考數(shù)學(xué)一輪復(fù)習(xí)提升訓(xùn)練2.2 基本不等式（精講）（原卷版）

2.2基本不等式（精講）（提升版）思維導(dǎo)圖思維導(dǎo)圖考點(diǎn)呈現(xiàn)考點(diǎn)呈現(xiàn)例題剖析例題剖析考點(diǎn)一基本不等式常考形式【例1-1】（2022·河北石家莊·高三階段練習(xí)）（多選）已知SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，則（

）A．SKIPIF1<0的最小值是1 B．SKIPIF1<0的最小值是SKIPIF1<0C．SKIPIF1<0的最小值是4 D．SKIPIF1<0的最小值是5【例1-2】（2022·全國(guó)·模擬預(yù)測(cè)）已知a，b為非負(fù)數(shù)，且滿(mǎn)足SKIPIF1<0，則SKIPIF1<0的最大值為（

）A．40 B．SKIPIF1<0 C．42 D．SKIPIF1<0【例1-3】（2022·全國(guó)·高三專(zhuān)題練習(xí)）已知正實(shí)數(shù)SKIPIF1<0滿(mǎn)足SKIPIF1<0，則SKIPIF1<0的最小值為（

）A．9 B．SKIPIF1<0 C．10 D．無(wú)最小值【例1-4】（2022·全國(guó)·高三專(zhuān)題練習(xí)）已知實(shí)數(shù)SKIPIF1<0，滿(mǎn)足SKIPIF1<0，若不等式SKIPIF1<0對(duì)任意的正實(shí)數(shù)SKIPIF1<0恒成立，那么實(shí)數(shù)m的最大值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．3 D．SKIPIF1<0【一隅三反】1．（2022·海南）（多選）已知SKIPIF1<0，SKIPIF1<0是正實(shí)數(shù)，則下列選項(xiàng)正確的是（

）A．若SKIPIF1<0，則SKIPIF1<0有最小值2B．若SKIPIF1<0，則SKIPIF1<0有最大值5C．若SKIPIF1<0，則SKIPIF1<0有最大值SKIPIF1<0D．SKIPIF1<0有最小值SKIPIF1<02．（2022·全國(guó)·高三專(zhuān)題練習(xí)（理））若a，b，c均為正實(shí)數(shù)，則SKIPIF1<0的最大值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·全國(guó)·高三專(zhuān)題練習(xí)）已知三次函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞增，則SKIPIF1<0最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·全國(guó)·高三專(zhuān)題練習(xí)）若兩個(gè)正實(shí)數(shù)SKIPIF1<0，SKIPIF1<0滿(mǎn)足SKIPIF1<0且存在這樣的SKIPIF1<0，SKIPIF1<0使不等式SKIPIF1<0有解，則實(shí)數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<05．（2022·全國(guó)·高三專(zhuān)題練習(xí)）若實(shí)數(shù)SKIPIF1<0滿(mǎn)足SKIPIF1<0，則SKIPIF1<0的最大值為_(kāi)_______.考點(diǎn)二基本不等式與其他知識(shí)綜合【例2-1】（2022·河南許昌）若直線SKIPIF1<0被圓SKIPIF1<0截得的弦長(zhǎng)為SKIPIF1<0，則SKIPIF1<0的最小值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【例2-2】．（2022·全國(guó)·高三專(zhuān)題練習(xí)）設(shè)SKIPIF1<0，則函數(shù)SKIPIF1<0的最大值為_(kāi)__________．【例2-3】（2022·山東·廣饒一中）直角三角形SKIPIF1<0中，SKIPIF1<0是斜邊SKIPIF1<0上一點(diǎn)，且滿(mǎn)足SKIPIF1<0，點(diǎn)SKIPIF1<0、SKIPIF1<0在過(guò)點(diǎn)SKIPIF1<0的直線上，若SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則下列結(jié)論錯(cuò)誤的是（

）A．SKIPIF1<0為常數(shù) B．SKIPIF1<0的最小值為SKIPIF1<0C．SKIPIF1<0的最小值為SKIPIF1<0 D．SKIPIF1<0、SKIPIF1<0的值可以為SKIPIF1<0，SKIPIF1<0【一隅三反】1．（2022·江西·臨川一中）已知SKIPIF1<0是正實(shí)數(shù)，函數(shù)SKIPIF1<0的圖象經(jīng)過(guò)點(diǎn)SKIPIF1<0，則SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．9 C．SKIPIF1<0 D．22．（2022·江西·模擬預(yù)測(cè)（理））在正項(xiàng)等比數(shù)列SKIPIF1<0中，SKIPIF1<0，前三項(xiàng)的和為7，若存在m，SKIPIF1<0使得SKIPIF1<0，則SKIPIF1<0的最小值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·安徽省舒城中學(xué)）如圖，在SKIPIF1<0中，SKIPIF1<0是線段SKIPIF1<0上的一點(diǎn)，且SKIPIF1<0，過(guò)點(diǎn)SKIPIF1<0的直線分別交直線SKIPIF1<0，SKIPIF1<0于點(diǎn)SKIPIF1<0，SKIPIF1<0，若SKIPIF1<0，SKIPIF1<0SKIPIF1<0，則SKIPIF1<0的最小值是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·廣東·廣州六中高一期末）己知第二象限角SKIPIF1<0的終邊上有異于原點(diǎn)的兩點(diǎn)SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．3 C．SKIPIF1<0 D．45．（2021·江蘇·揚(yáng)州大學(xué)附屬中學(xué)）不等式SKIPIF1<0的解集為SKIPIF1<0，則SKIPIF1<0的最大值為_(kāi)___________.6．（2022·安徽·合肥一中）已知圓SKIPIF1<0的半徑為3，SKIPIF1<0，SKIPIF1<0為該圓的兩條切線，SKIPIF1<0為切點(diǎn)，則SKIPIF1<0的最小值為_(kāi)__________.7．（2021·四川達(dá)州·一模（文））定義在SKIPIF1<0上的函數(shù)SKIPIF1<0滿(mǎn)足SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0.設(shè)SKIPIF1<0在SKIPIF1<0上最小值為SKIPIF1<0，則SKIPIF1<0___________.考點(diǎn)三連用兩次基本不等式【例3】（2021·廣東河源·模擬預(yù)測(cè)）函數(shù)SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·全國(guó)·高三專(zhuān)題練習(xí)）若a，SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的最大值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．2 D．4