專題06利用導(dǎo)數(shù)研究函數(shù)的最值專項(xiàng)突破一函數(shù)最值與極值關(guān)系一、單選題1．SKIPIF1<0是定義在SKIPIF1<0的函數(shù)，導(dǎo)函數(shù)SKIPIF1<0在SKIPIF1<0內(nèi)的圖象如圖所示，則下列說法有誤的是（

）A．函數(shù)SKIPIF1<0在SKIPIF1<0一定存在最小值B．函數(shù)SKIPIF1<0在SKIPIF1<0只有一個(gè)極小值點(diǎn)C．函數(shù)SKIPIF1<0在SKIPIF1<0有兩個(gè)極大值點(diǎn)D．函數(shù)SKIPIF1<0在SKIPIF1<0可能沒有零點(diǎn)【解析】由導(dǎo)函數(shù)的圖像可知原函數(shù)的圖像如圖所示，對于A：不確定端點(diǎn)及極小值的大小，同時(shí)端點(diǎn)值取不到，故不一定有最小值，A錯(cuò)誤；對于B：由圖像可知只有一個(gè)極小值，B正確；對于C：由圖像可知有兩個(gè)極大值，C正確；對于D：函數(shù)圖像極值大小不確定且可以上下平移，故在SKIPIF1<0可能沒有零點(diǎn)，D正確.故選：A.2．已知函數(shù)SKIPIF1<0的導(dǎo)函數(shù)圖像，如圖所示，那么函數(shù)SKIPIF1<0（

）A．在SKIPIF1<0上單調(diào)遞增 B．在SKIPIF1<0處取得極小值C．在SKIPIF1<0處切線斜率取得最大值 D．在SKIPIF1<0處取得最大值【解析】結(jié)合圖像易知，當(dāng)SKIPIF1<0時(shí)，函數(shù)SKIPIF1<0是減函數(shù)，當(dāng)SKIPIF1<0時(shí)，函數(shù)SKIPIF1<0取極小值，當(dāng)SKIPIF1<0時(shí)，函數(shù)SKIPIF1<0是增函數(shù)，當(dāng)SKIPIF1<0時(shí)，函數(shù)SKIPIF1<0取極大值，不一定是最大值，當(dāng)SKIPIF1<0時(shí)，函數(shù)SKIPIF1<0是減函數(shù)，結(jié)合上述易知，A、B、D錯(cuò)誤，因?yàn)楹瘮?shù)在某點(diǎn)處的導(dǎo)函數(shù)值即函數(shù)在這點(diǎn)處的切線斜率，所以由圖像易知，在SKIPIF1<0處切線斜率取得最大值，C正確，故選：C.二、多選題3．下列關(guān)于極值點(diǎn)的說法正確的是（

）A．若函數(shù)SKIPIF1<0既有極大值又有極小值，則該極大值一定大于極小值B．SKIPIF1<0在任意給定區(qū)間SKIPIF1<0上必存在最小值C．SKIPIF1<0的最大值就是該函數(shù)的極大值D．定義在SKIPIF1<0上的函數(shù)可能沒有極值點(diǎn)，也可能存在無數(shù)個(gè)極值點(diǎn)【解析】A選項(xiàng)，例如SKIPIF1<0，在SKIPIF1<0處取得極小值SKIPIF1<0，在SKIPIF1<0處取得極大值SKIPIF1<0，而SKIPIF1<0，故極大值不一定大于極小值，A錯(cuò)誤，C選項(xiàng)，SKIPIF1<0，函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞增，在SKIPIF1<0上單調(diào)遞減，根據(jù)極值的定義可知：SKIPIF1<0在SKIPIF1<0處取得極大值，也是最大值，C正確；對于D，SKIPIF1<0無極值點(diǎn)，SKIPIF1<0有無數(shù)個(gè)極值點(diǎn)，D正確；SKIPIF1<0在R上為連續(xù)函數(shù)，因?yàn)檫B續(xù)函數(shù)在閉區(qū)間上必定存在最值，所以B正確；故選：BCD．4．下列說法正確的是（

）A．極值點(diǎn)處的導(dǎo)數(shù)值為SKIPIF1<0B．極大值一定比極小值大C．可導(dǎo)函數(shù)在閉區(qū)間內(nèi)的最大值必在極值點(diǎn)或區(qū)間端點(diǎn)處取得D．如果函數(shù)SKIPIF1<0的定義域?yàn)镾KIPIF1<0，且SKIPIF1<0在SKIPIF1<0上遞減，在SKIPIF1<0上遞增，則SKIPIF1<0的最小值為SKIPIF1<0【解析】對于A，函數(shù)的極值點(diǎn)處未必可導(dǎo)，如SKIPIF1<0是SKIPIF1<0的極值點(diǎn)，但SKIPIF1<0在SKIPIF1<0處不可導(dǎo)，A錯(cuò)誤；對于B，函數(shù)的極大值和極小值可能有無數(shù)個(gè)，是由函數(shù)的單調(diào)性得到的，大小關(guān)系不確定，B錯(cuò)誤；對于C，可導(dǎo)函數(shù)在閉區(qū)間內(nèi)連續(xù)，其最值必在極值點(diǎn)或區(qū)間端點(diǎn)處取得，則最大值也必在極值點(diǎn)或區(qū)間端點(diǎn)處，C正確；對于D，由單調(diào)性可知，函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0內(nèi)有唯一的極小值點(diǎn)SKIPIF1<0，且根據(jù)單調(diào)性可知其為最小值點(diǎn)，即最小值為SKIPIF1<0，D正確.故選：CD.5．（多選）下列結(jié)論中不正確的是（

）.A．若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上有最大值，則這個(gè)最大值一定是函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的極大值B．若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上有最小值，則這個(gè)最小值一定是函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的極小值C．若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上有最值，則最值一定在SKIPIF1<0或SKIPIF1<0處取得D．若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0內(nèi)連續(xù)，則SKIPIF1<0在區(qū)間SKIPIF1<0內(nèi)必有最大值與最小值【解析】若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上有最值，則最值可能在極值點(diǎn)或區(qū)間端點(diǎn)處取得，故A，B，C都不正確；函數(shù)在閉區(qū)間上一定有最值，故D正確.故選：ABC.專項(xiàng)突破二求具體函數(shù)最值一、單選題1．SKIPIF1<0在區(qū)間SKIPIF1<0上的最大值是（

）A．1 B．2 C．3 D．4【解析】SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，∴SKIPIF1<0在SKIPIF1<0上單調(diào)遞增，在SKIPIF1<0上單調(diào)遞減；∴SKIPIF1<0在區(qū)間SKIPIF1<0上的最大值為SKIPIF1<0．故選：B．二、多選題2．已知函數(shù)SKIPIF1<0，則（

）A．SKIPIF1<0在SKIPIF1<0上單調(diào)遞增B．SKIPIF1<0在SKIPIF1<0上單調(diào)遞減C．SKIPIF1<0D．SKIPIF1<0的極小值大于0【解析】因?yàn)镾KIPIF1<0，故SKIPIF1<0，即SKIPIF1<0，故SKIPIF1<0關(guān)于SKIPIF1<0對稱.故可設(shè)SKIPIF1<0SKIPIF1<0，即SKIPIF1<0，為偶函數(shù)，則SKIPIF1<0，畫出SKIPIF1<0與SKIPIF1<0，考慮SKIPIF1<0時(shí)的情況，易得兩圖象交點(diǎn)為SKIPIF1<0與SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0在SKIPIF1<0上方，故SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0在SKIPIF1<0下，故SKIPIF1<0.故當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0單調(diào)遞增，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0單調(diào)遞減.又SKIPIF1<0，故SKIPIF1<0為SKIPIF1<0的圖象往左平移SKIPIF1<0個(gè)單位，故當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0單調(diào)遞增，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0單調(diào)遞減.又SKIPIF1<0關(guān)于SKIPIF1<0對稱，故當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0單調(diào)遞增，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0單調(diào)遞減.故A正確，B錯(cuò)誤；又SKIPIF1<0最大值SKIPIF1<0SKIPIF1<0，故C正確；又極小值SKIPIF1<0，故D正確故選：ACD三、填空題3．函數(shù)SKIPIF1<0的最大值為________．【解析】SKIPIF1<0，所以SKIPIF1<0在SKIPIF1<0遞增，在SKIPIF1<0遞減，所以當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0取得最大值為SKIPIF1<0.4．函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的最小值為__________.【解析】由SKIPIF1<0，得SKIPIF1<0，當(dāng)且僅當(dāng)SKIPIF1<0時(shí)取等號，即SKIPIF1<0取等號，因?yàn)镾KIPIF1<0，所以函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞增，所以當(dāng)SKIPIF1<0時(shí)，函數(shù)取得最小值05．SKIPIF1<0，SKIPIF1<0的最小值為___________．【解析】令SKIPIF1<0，則SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0單調(diào)增，SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，令SKIPIF1<0，SKIPIF1<0，SKIPIF1<0時(shí)SKIPIF1<0，SKIPIF1<0遞減，SKIPIF1<0時(shí)SKIPIF1<0，SKIPIF1<0遞增，∴SKIPIF1<0，綜上：SKIPIF1<06．已知SKIPIF1<0是奇函數(shù)，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0的最小值為________．【解析】SKIPIF1<0，SKIPIF1<0，所以SKIPIF1<0，又因?yàn)镾KIPIF1<0是奇函數(shù)，所以SKIPIF1<0，所以當(dāng)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，令SKIPIF1<0，所以SKIPIF1<0，則SKIPIF1<0在SKIPIF1<0上單調(diào)遞減，在SKIPIF1<0上單調(diào)遞增，所以SKIPIF1<0.所以當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0的最小值為1.四、解答題7．已知函數(shù)SKIPIF1<0．(1)求函數(shù)SKIPIF1<0在SKIPIF1<0處的切線方程；(2)求函數(shù)SKIPIF1<0在SKIPIF1<0上的最大值與最小值．【解析】(1)由SKIPIF1<0得SKIPIF1<0,SKIPIF1<0又SKIPIF1<0,所以函數(shù)SKIPIF1<0在SKIPIF1<0處的切線方程為:SKIPIF1<0,即SKIPIF1<0(2)由SKIPIF1<0,令SKIPIF1<0解得SKIPIF1<0令SKIPIF1<0解得SKIPIF1<0,所以SKIPIF1<0在SKIPIF1<0上單調(diào)遞增,在SKIPIF1<0上單調(diào)遞減.所以當(dāng)SKIPIF1<0時(shí),SKIPIF1<0最小,且最小值為SKIPIF1<0,SKIPIF1<0,SKIPIF1<0,故最大值為SKIPIF1<08．已知SKIPIF1<0的一個(gè)極值點(diǎn)為2.（1）求函數(shù)SKIPIF1<0的單調(diào)區(qū)間；（2）求函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的最值.【解析】（1）因?yàn)镾KIPIF1<0，所以SKIPIF1<0，因?yàn)镾KIPIF1<0的一個(gè)極值點(diǎn)為2，所以SKIPIF1<0，解得SKIPIF1<0，此時(shí)SKIPIF1<0，SKIPIF1<0，令SKIPIF1<0，得SKIPIF1<0或SKIPIF1<0，令SKIPIF1<0，得SKIPIF1<0；令SKIPIF1<0，得SKIPIF1<0或SKIPIF1<0，故函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞減，在區(qū)間SKIPIF1<0，SKIPIF1<0上單調(diào)遞增.（2）由（1）知，SKIPIF1<0在SKIPIF1<0上為增函數(shù)，在SKIPIF1<0上為減函數(shù)，所以SKIPIF1<0是函數(shù)SKIPIF1<0的極大值點(diǎn)，又SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，所以函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的最小值為SKIPIF1<0，最大值為SKIPIF1<0.9．已知函數(shù)SKIPIF1<0．(1)求SKIPIF1<0的單調(diào)區(qū)間；(2)求SKIPIF1<0在區(qū)間SKIPIF1<0上的最值．【解析】(1)由題意知：SKIPIF1<0．令SKIPIF1<0，解得SKIPIF1<0．SKIPIF1<0把SKIPIF1<0定義域劃分成兩個(gè)區(qū)間，SKIPIF1<0在各區(qū)間上的正負(fù)，以及SKIPIF1<0的單調(diào)性如下表所示.SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<00SKIPIF1<0SKIPIF1<0單調(diào)遞減單調(diào)遞增所以SKIPIF1<0的單調(diào)遞減區(qū)間為SKIPIF1<0，單調(diào)遞增區(qū)間為SKIPIF1<0．(2)結(jié)合（1）的結(jié)論，列表如下：SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<00SKIPIF1<0SKIPIF1<0SKIPIF1<0單調(diào)遞減SKIPIF1<0單調(diào)遞增SKIPIF1<0所以SKIPIF1<0在區(qū)間SKIPIF1<0上的最小值是SKIPIF1<0，最大值是SKIPIF1<0．10．已知函數(shù)SKIPIF1<0，曲線SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線方程為SKIPIF1<0(1)求a，b的值；(2)求SKIPIF1<0在SKIPIF1<0上的最大值和最小值.【解析】(1)依題意可知點(diǎn)SKIPIF1<0為切點(diǎn)，代入切線方程SKIPIF1<0可得SKIPIF1<0∴SKIPIF1<0，即SKIPIF1<0，又由SKIPIF1<0得，SKIPIF1<0，而由切線SKIPIF1<0的斜率可知SKIPIF1<0，∴SKIPIF1<0，即SKIPIF1<0，由SKIPIF1<0，解得SKIPIF1<0(2)由（1）知SKIPIF1<0SKIPIF1<0，令SKIPIF1<0，得SKIPIF1<0或SKIPIF1<0，當(dāng)x變化時(shí)，SKIPIF1<0，SKIPIF1<0的變化情況如下表：xSKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<02SKIPIF1<00SKIPIF1<00＋SKIPIF1<013單調(diào)遞減SKIPIF1<0單調(diào)遞增13∴SKIPIF1<0最大值為13，最小值為SKIPIF1<011．已知SKIPIF1<0為自然對數(shù)的底.(1)求SKIPIF1<0在SKIPIF1<0處的切線方程；(2)求SKIPIF1<0在SKIPIF1<0上的最小值和最大值.【解析】(1)因?yàn)镾KIPIF1<0，所以SKIPIF1<0，則SKIPIF1<0，SKIPIF1<0，故SKIPIF1<0在SKIPIF1<0處的切線方程為SKIPIF1<0.(2)由（1）知，SKIPIF1<0，由SKIPIF1<0，SKIPIF1<0，故SKIPIF1<0在區(qū)間SKIPIF1<0上為增函數(shù)，在區(qū)間SKIPIF1<0上為減函數(shù)，且SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，故SKIPIF1<0在SKIPIF1<0上的最小值為SKIPIF1<0，最大值為SKIPIF1<0.12．已知函數(shù)SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0的極小值為SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0有極大值．(1)求函數(shù)SKIPIF1<0；(2)存在SKIPIF1<0，使得SKIPIF1<0成立，求實(shí)數(shù)SKIPIF1<0的取值范圍．【解析】(1)∵SKIPIF1<0，由SKIPIF1<0，得SKIPIF1<0且SKIPIF1<0，解得SKIPIF1<0，SKIPIF1<0，又SKIPIF1<0，∴SKIPIF1<0，經(jīng)檢驗(yàn)SKIPIF1<0，SKIPIF1<0時(shí)，SKIPIF1<0滿足題意,∴SKIPIF1<0；(2)存在SKIPIF1<0，使得SKIPIF1<0，等價(jià)于SKIPIF1<0，∵SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，∴SKIPIF1<0在SKIPIF1<0上遞減，在SKIPIF1<0上遞增，又SKIPIF1<0，SKIPIF1<0，∴SKIPIF1<0在SKIPIF1<0上的最小值為SKIPIF1<0，∴SKIPIF1<0，解得SKIPIF1<0或SKIPIF1<0，所以SKIPIF1<0的取值范圍是SKIPIF1<0．13．已知函數(shù)SKIPIF1<0.(1)求SKIPIF1<0的最小值；(2)證明：SKIPIF1<0.【解析】(1)由題意可得SKIPIF1<0.由SKIPIF1<0，得SKIPIF1<0；由SKIPIF1<0，得SKIPIF1<0.SKIPIF1<0在SKIPIF1<0上單調(diào)遞減，在SKIPIF1<0上單調(diào)遞增，故SKIPIF1<0.(2)證明：要證SKIPIF1<0，即證SKIPIF1<0，即證SKIPIF1<0.設(shè)SKIPIF1<0，則SKIPIF1<0，由SKIPIF1<0，得SKIPIF1<0，由SKIPIF1<0，得SKIPIF1<0，則SKIPIF1<0，當(dāng)且僅當(dāng)SKIPIF1<0時(shí)，等號成立.設(shè)SKIPIF1<0，則SKIPIF1<0.由（1）可知當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0.由SKIPIF1<0，得SKIPIF1<0，由SKIPIF1<0，得SKIPIF1<0，則SKIPIF1<0，當(dāng)且僅當(dāng)SKIPIF1<0時(shí)，等號成立.因?yàn)镾KIPIF1<0與SKIPIF1<0等號成立的條件不同，所以SKIPIF1<0，即SKIPIF1<0.專項(xiàng)突破三求含參函數(shù)最值一、單選題1．函數(shù)SKIPIF1<0在SKIPIF1<0上的最大值為4，則SKIPIF1<0的值為（

）A．7 B．SKIPIF1<0 C．3 D．4【解析】∵SKIPIF1<0，∴SKIPIF1<0∴導(dǎo)數(shù)SKIPIF1<0在SKIPIF1<0時(shí)，SKIPIF1<0，SKIPIF1<0單調(diào)遞減；導(dǎo)數(shù)SKIPIF1<0在SKIPIF1<0時(shí)，SKIPIF1<0，SKIPIF1<0單調(diào)遞增；∵SKIPIF1<0，SKIPIF1<0，SKIPIF1<0∴SKIPIF1<0在SKIPIF1<0處取得最大值為SKIPIF1<0，即SKIPIF1<0，故選：D.2．函數(shù)SKIPIF1<0的最大值為（

）A．a(chǎn) B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【解析】SKIPIF1<0,則SKIPIF1<0,所以當(dāng)SKIPIF1<0時(shí),SKIPIF1<0,當(dāng)SKIPIF1<0時(shí),SKIPIF1<0,所以SKIPIF1<0在SKIPIF1<0上單調(diào)遞增,在SKIPIF1<0上單調(diào)遞減,所以SKIPIF1<0,故選:D.二、多選題3．已知函數(shù)SKIPIF1<0，SKIPIF1<0的圖像分別與直線SKIPIF1<0交于A，B兩點(diǎn)，則SKIPIF1<0的值可為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．2【解析】由題意得SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，易知SKIPIF1<0，所以SKIPIF1<0，SKIPIF1<0.令SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0，令SKIPIF1<0，得SKIPIF1<0.所以當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0；當(dāng)SKIPIF1<0，SKIPIF1<0，所以SKIPIF1<0，SKIPIF1<0在SKIPIF1<0上單調(diào)遞減，在SKIPIF1<0上單調(diào)遞增.所以SKIPIF1<0，故選：AB三、填空題4．已知，為正實(shí)數(shù)，函數(shù)在上的最大值為，則在上的最小值為_________________________．【解析】∵，為正實(shí)數(shù)，∴SKIPIF1<0，，SKIPIF1<0即SKIPIF1<0.則在上的最小值為SKIPIF1<0.四、解答題5．已知函數(shù)SKIPIF1<0．(1)求函數(shù)SKIPIF1<0的單調(diào)區(qū)間；(2)求函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的最小值．【解析】(1)SKIPIF1<0則SKIPIF1<0，令SKIPIF1<0，則SKIPIF1<0或SKIPIF1<0∴SKIPIF1<0在SKIPIF1<0，SKIPIF1<0上遞增，在SKIPIF1<0遞減(2)由（1）可知：SKIPIF1<0在SKIPIF1<0上遞增，在SKIPIF1<0遞減，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0在SKIPIF1<0遞減∴函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的最小值為SKIPIF1<0；當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0在SKIPIF1<0上遞增，在SKIPIF1<0遞減∴函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的最小值為SKIPIF1<0．綜上所述：當(dāng)SKIPIF1<0時(shí)，函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的最小值為SKIPIF1<0；當(dāng)SKIPIF1<0時(shí)，函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的最小值為SKIPIF1<0．6．已知函數(shù)SKIPIF1<0，SKIPIF1<0.(1)討論SKIPIF1<0的單調(diào)性；(2)當(dāng)SKIPIF1<0時(shí)，記SKIPIF1<0在區(qū)間SKIPIF1<0的最大值為M，最小值為N，求SKIPIF1<0的取值范圍.【解析】(1)因?yàn)镾KIPIF1<0，故可得SKIPIF1<0SKIPIF1<0，令SKIPIF1<0SKIPIF1<0，可得SKIPIF1<0或SKIPIF1<0；當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0SKIPIF1<0，此時(shí)SKIPIF1<0在SKIPIF1<0上單調(diào)遞增；當(dāng)SKIPIF1<0時(shí)，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0SKIPIF1<0，SKIPIF1<0單調(diào)遞增；當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0SKIPIF1<0，SKIPIF1<0單調(diào)遞減；當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0SKIPIF1<0，SKIPIF1<0單調(diào)遞增；當(dāng)SKIPIF1<0時(shí)，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0SKIPIF1<0，SKIPIF1<0單調(diào)遞增；當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0SKIPIF1<0，SKIPIF1<0單調(diào)遞減；當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0SKIPIF1<0，SKIPIF1<0單調(diào)遞增.綜上所述：當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0在SKIPIF1<0上單調(diào)遞增；當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0在SKIPIF1<0和SKIPIF1<0單調(diào)遞增，在SKIPIF1<0單調(diào)遞減；當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0在SKIPIF1<0和SKIPIF1<0單調(diào)遞增，在SKIPIF1<0單調(diào)遞減.(2)由（1）可知：當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0在SKIPIF1<0單調(diào)遞減，在SKIPIF1<0單調(diào)遞增又SKIPIF1<0，SKIPIF1<0SKIPIF1<0，故SKIPIF1<0在SKIPIF1<0單調(diào)遞減，在SKIPIF1<0單調(diào)遞增.則SKIPIF1<0的最小值SKIPIF1<0；又SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0的最大值SKIPIF1<0，此時(shí)SKIPIF1<0；當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0的最大值SKIPIF1<0，此時(shí)SKIPIF1<0，令SKIPIF1<0，則SKIPIF1<0，所以SKIPIF1<0在SKIPIF1<0上單調(diào)遞減，所以SKIPIF1<0，所以SKIPIF1<0；所以SKIPIF1<0的取值范圍為SKIPIF1<0.7．已知函數(shù)SKIPIF1<0．（1）討論SKIPIF1<0的單調(diào)性；（2）當(dāng)SKIPIF1<0時(shí)，求SKIPIF1<0在區(qū)間SKIPIF1<0上的最大值．【解析】（1）由題意得：SKIPIF1<0定義域?yàn)镾KIPIF1<0，SKIPIF1<0，①當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，SKIPIF1<0在SKIPIF1<0上單調(diào)遞增；②當(dāng)SKIPIF1<0時(shí)，令SKIPIF1<0得：SKIPIF1<0，列表如下：SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0＋SKIPIF1<0－SKIPIF1<0遞增極大值遞減SKIPIF1<0在SKIPIF1<0上單調(diào)遞增，在SKIPIF1<0上單調(diào)遞減；綜上所述：當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0在SKIPIF1<0上單調(diào)遞增；當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0在SKIPIF1<0上單調(diào)遞增，在SKIPIF1<0上單調(diào)遞減.（2）當(dāng)SKIPIF1<0時(shí)，由（1）知：①當(dāng)SKIPIF1<0，即SKIPIF1<0時(shí)，SKIPIF1<0在SKIPIF1<0上單調(diào)遞減，則SKIPIF1<0；②當(dāng)SKIPIF1<0，即SKIPIF1<0時(shí)，SKIPIF1<0在SKIPIF1<0上單調(diào)遞增，在SKIPIF1<0上單調(diào)遞減，SKIPIF1<0；③當(dāng)SKIPIF1<0，即SKIPIF1<0時(shí)，SKIPIF1<0在SKIPIF1<0上單調(diào)遞增，則SKIPIF1<0；綜上所述：SKIPIF1<0.8．已知函數(shù)SKIPIF1<0，其中SKIPIF1<0．（1）求SKIPIF1<0的單調(diào)區(qū)間；（2）求SKIPIF1<0在SKIPIF1<0上的最大值【解析】（1）因?yàn)镾KIPIF1<0定義域?yàn)镾KIPIF1<0，所以SKIPIF1<0，令SKIPIF1<0，SKIPIF1<0且SKIPIF1<0，SKIPIF1<0，解得SKIPIF1<0，令SKIPIF1<0，SKIPIF1<0，解得SKIPIF1<0或SKIPIF1<0，SKIPIF1<0在SKIPIF1<0和SKIPIF1<0上單調(diào)遞減，在SKIPIF1<0上單調(diào)遞增．即SKIPIF1<0的單調(diào)遞減區(qū)間為SKIPIF1<0和SKIPIF1<0，單調(diào)遞增區(qū)間為SKIPIF1<0．（2）①當(dāng)SKIPIF1<0，即SKIPIF1<0時(shí)，SKIPIF1<0在SKIPIF1<0內(nèi)是減函數(shù)．SKIPIF1<0在SKIPIF1<0上SKIPIF1<0；②當(dāng)SKIPIF1<0，即SKIPIF1<0時(shí)，SKIPIF1<0在SKIPIF1<0上單調(diào)遞增，在SKIPIF1<0上單調(diào)遞減．SKIPIF1<0在SKIPIF1<0上SKIPIF1<0；③當(dāng)SKIPIF1<0，即SKIPIF1<0時(shí)，SKIPIF1<0在SKIPIF1<0上單調(diào)遞增，SKIPIF1<0在SKIPIF1<0上SKIPIF1<0．綜上所述，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0在SKIPIF1<0上的最大值為SKIPIF1<0；當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0在SKIPIF1<0上的最大值為SKIPIF1<0；當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0在SKIPIF1<0上的最大值為SKIPIF1<0．9．已知函數(shù)SKIPIF1<0．(1)當(dāng)SKIPIF1<0時(shí)，求曲線SKIPIF1<0在SKIPIF1<0處的切線方程；(2)求函數(shù)SKIPIF1<0的單調(diào)區(qū)間；(3)當(dāng)SKIPIF1<0時(shí)，求函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的最小值．【解析】(1)當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0

，SKIPIF1<0SKIPIF1<0，SKIPIF1<0，故切線方程為：SKIPIF1<0，(2)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0SKIPIF1<0①當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，SKIPIF1<0僅有單調(diào)遞增區(qū)間，其為：SKIPIF1<0②當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，SKIPIF1<0當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0；當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0SKIPIF1<0的單調(diào)遞增區(qū)間為：SKIPIF1<0，單調(diào)遞減區(qū)間為：SKIPIF1<0③當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，SKIPIF1<0當(dāng)SKIPIF1<0時(shí)SKIPIF1<0；當(dāng)SKIPIF1<0時(shí)SKIPIF1<0SKIPIF1<0的單調(diào)遞增區(qū)間為：SKIPIF1<0，單調(diào)遞減區(qū)間為：SKIPIF1<0綜上所述：當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0僅有單調(diào)遞增區(qū)間，單調(diào)遞增區(qū)間為：SKIPIF1<0當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0的單調(diào)遞增區(qū)間為：SKIPIF1<0，單調(diào)遞減區(qū)間為：SKIPIF1<0當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0的單調(diào)遞增區(qū)間為：SKIPIF1<0，單調(diào)遞減區(qū)間為：SKIPIF1<0(3)當(dāng)SKIPIF1<0時(shí)，由（2）中③知SKIPIF1<0在SKIPIF1<0上單調(diào)單調(diào)遞減，在SKIPIF1<0上單調(diào)遞增，∴①當(dāng)SKIPIF1<0，即SKIPIF1<0時(shí)，SKIPIF1<0在SKIPIF1<0上單調(diào)遞增，SKIPIF1<0，②當(dāng)SKIPIF1<0，即SKIPIF1<0時(shí)，SKIPIF1<0在SKIPIF1<0上單調(diào)遞減，在SKIPIF1<0上單調(diào)遞增，∴SKIPIF1<0，③當(dāng)SKIPIF1<0，即SKIPIF1<0時(shí)，SKIPIF1<0在SKIPIF1<0上單調(diào)遞減，∴SKIPIF1<0.．SKIPIF1<010．已知函數(shù)SKIPIF1<0(1)當(dāng)SKIPIF1<0時(shí)，求過點(diǎn)SKIPIF1<0的切線方程；(2)求函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0的最小值．【解析】(1)當(dāng)SKIPIF1<0時(shí)，函數(shù)SKIPIF1<0，可得SKIPIF1<0，設(shè)切點(diǎn)坐標(biāo)為SKIPIF1<0，則切線的斜率為SKIPIF1<0，所以切線方程為SKIPIF1<0，將點(diǎn)SKIPIF1<0代入切線方程，可得SKIPIF1<0，即SKIPIF1<0，解得SKIPIF1<0，則SKIPIF1<0，所以切線方程為SKIPIF1<0.(2)由SKIPIF1<0，可得SKIPIF1<0，令SKIPIF1<0，解得SKIPIF1<0，且SKIPIF1<0①若SKIPIF1<0時(shí)，即SKIPIF1<0時(shí)，此時(shí)SKIPIF1<0，SKIPIF1<0單調(diào)遞增，所以SKIPIF1<0；②若SKIPIF1<0時(shí)，即SKIPIF1<0時(shí)，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，SKIPIF1<0單調(diào)遞減；當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，SKIPIF1<0單調(diào)遞增，所以SKIPIF1<0；③若SKIPIF1<0時(shí)，即SKIPIF1<0時(shí)，此時(shí)SKIPIF1<0，SKIPIF1<0單調(diào)遞減，所以SKIPIF1<0，綜上可得，當(dāng)SKIPIF1<0時(shí)，最小值為SKIPIF1<0；當(dāng)SKIPIF1<0時(shí)，最小值為SKIPIF1<0；當(dāng)SKIPIF1<0時(shí)，最小值為SKIPIF1<0.專項(xiàng)突破四根據(jù)函數(shù)最值求參一、單選題1．函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的最大值是SKIPIF1<0，則SKIPIF1<0的值為()A．3 B．1C．2 D．－1【解析】由題意可知，SKIPIF1<0，令SKIPIF1<0，解得SKIPIF1<0或SKIPIF1<0（舍）.當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0；當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0；所以函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞減，在SKIPIF1<0上單調(diào)遞增.所以SKIPIF1<0,SKIPIF1<0,SKIPIF1<0，則SKIPIF1<0最大，所以當(dāng)SKIPIF1<0時(shí)，函數(shù)SKIPIF1<0取得最大值為SKIPIF1<0.由題意可知，SKIPIF1<0，解得SKIPIF1<0,所以SKIPIF1<0的值為SKIPIF1<0.故選：B.2．若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0內(nèi)既存在最大值也存在最小值，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【解析】由SKIPIF1<0得SKIPIF1<0或SKIPIF1<0，可以判斷SKIPIF1<0在SKIPIF1<0處取得極小值SKIPIF1<0，在SKIPIF1<0處取得極大值SKIPIF1<0.令SKIPIF1<0，得SKIPIF1<0或SKIPIF1<0，令SKIPIF1<0，得SKIPIF1<0或SKIPIF1<0，由題意知函數(shù)SKIPIF1<0在開區(qū)間SKIPIF1<0內(nèi)的最大、最小值只能在SKIPIF1<0和SKIPIF1<0處取得，結(jié)合函數(shù)SKIPIF1<0的圖象可得：SKIPIF1<0，解得SKIPIF1<0，故SKIPIF1<0的取值范圍是SKIPIF1<0.故選：A3．函數(shù)SKIPIF1<0，若SKIPIF1<0在SKIPIF1<0上有最小值，則實(shí)數(shù)a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【解析】由題意，函數(shù)SKIPIF1<0，可得SKIPIF1<0，若SKIPIF1<0時(shí)，當(dāng)SKIPIF1<0時(shí)，可得SKIPIF1<0，SKIPIF1<0在SKIPIF1<0上單調(diào)遞減，此時(shí)函數(shù)SKIPIF1<0在SKIPIF1<0沒有最小值，不符合題意；當(dāng)SKIPIF1<0時(shí)，令SKIPIF1<0，即SKIPIF1<0，即SKIPIF1<0與SKIPIF1<0的交點(diǎn)，畫出函數(shù)SKIPIF1<0與SKIPIF1<0的圖象，如圖所示，結(jié)合圖象，可得存在SKIPIF1<0，使得SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，SKIPIF1<0單調(diào)遞減；當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，SKIPIF1<0單調(diào)遞增，此時(shí)函數(shù)SKIPIF1<0在SKIPIF1<0上有最小值，符合題意，綜上可得，實(shí)數(shù)a的取值范圍是SKIPIF1<0.故選：A.4．若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上存在最小值，則實(shí)數(shù)SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【解析】由函數(shù)SKIPIF1<0，可得SKIPIF1<0，且SKIPIF1<0在區(qū)間SKIPIF1<0上存在最小值，即SKIPIF1<0在區(qū)間SKIPIF1<0上存在SKIPIF1<0，使得SKIPIF1<0且SKIPIF1<0，SKIPIF1<0，設(shè)SKIPIF1<0，即滿足SKIPIF1<0，且SKIPIF1<0，可得SKIPIF1<0，解得SKIPIF1<0，即實(shí)數(shù)SKIPIF1<0的取值范圍是SKIPIF1<0.故選：D.5．若對任意的實(shí)數(shù)SKIPIF1<0恒成立，則實(shí)數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【解析】令SKIPIF1