導(dǎo)數(shù)的應(yīng)用,判斷函數(shù)的單調(diào)性,典型題型有答案

1、賈老師數(shù)學精講精練系列導(dǎo)數(shù)的應(yīng)用，判斷函數(shù)的單調(diào)性題型一、基礎(chǔ)題型例題1.函數(shù)f (x)A.(2,)練習A.(1.1.函數(shù),2)23x1是減函數(shù)的區(qū)間為(,2)C.(,0)-.X 、,、一一.、一-.3XB.(f(x) (X 3)e的單調(diào)遞增區(qū)間是(B(0,3)C.(1,4)【答案:D.(0,2)【答案：D.(2,D】D】)練習1.2.函數(shù)f (x) XlnX的單調(diào)遞增區(qū)間是1【答案：(丄，)】e練習1.3.函數(shù)A(練習1,11.4.函數(shù)3A(,)2 21 2X lnx的單調(diào)遞減區(qū)間為()【答案:2B.(0,1XCOSXB.( ,2C.1,)D.(0,SinX在下面那個區(qū)間內(nèi)是增函數(shù)(35C.

2、(,)D.(22 2B】)【答案：B】,3 )題型二、含有參數(shù)例題2.設(shè)函數(shù)f (x)2 ax【答案：單增(若a0,求函數(shù)謁】f (X)的單調(diào)區(qū)間。練習2.1.設(shè)函數(shù)f (X)【答案：單增(1m,113X3m)；單減(X2(m21)x(x R),其中mOo求函數(shù)f (X)的單調(diào)區(qū)間。,1m),(1 m,)】練習2.2.已知函數(shù)f (X)【答案：單增(2a,0),(a,1ax3單減(a2x2 a4(a0)。,2a),(0,a)】求函數(shù)f (X)的單調(diào)區(qū)間。練習2.3.設(shè)函數(shù)f(x) a2ln【答案：單增(0,a)；單減(a,X2 ax,a0 O求函數(shù)f (X)的單調(diào)區(qū)間。 )】練習2.4.已知a

3、0 ,函數(shù)f (x)ln Xax2 o求函數(shù)f(x)的單調(diào)區(qū)間。r r Oar Pa【答案：單增(0,4);單減(上2a2a)】題型三、含參討論例題3.已知函數(shù)f(x) 4x3 3tx2 6t2x【答案：當tv時，單增( 丄),(t,2當t0時，單增(，t),(上，2練習 3.1.設(shè)函數(shù) f(x) 2x3 3(a 1)x2 【答案：當a 1時，單增R;當 a1 時，單增(,0),(a 1,t 1,x R。當t 0時，求函數(shù)f (x)的單調(diào)區(qū)間。),單減(一，t)；2),單減(t,-)】21 ,其中a 1 o求函數(shù)f(x)的單調(diào)區(qū)間。),單減(0,a1)】323練習32已知函數(shù)f() ax 3x 1 。討論函數(shù)f(x)的單調(diào)區(qū)間。a22【答案：當a0時，單增(，0),(,),單減(0,);aa22當av0時，單增(-,0),單減(,-),(0,)】aa練習3.3.設(shè)函數(shù)f(x) ex ax 2。求函數(shù)f(x)的單調(diào)區(qū)間?！敬鸢福寒攁 0時，單增R;當a0時，單增(In a,),單減(，In a)】練習34已知函數(shù)f() (X 2)ex a(x 1)2 ,討論函數(shù)f(x)的單調(diào)區(qū)間。 【答案：當a 0時，單增(1,),單減(，1);e當 一V av 0 時，單增(，ln( 2a), (1,),單減(ln( 2a),1)；2當a