2023届山东省高三二模三模汇编（含解析）（解析版）导数小题

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⚪13ᦪ⚪ஹᓫ⌱⚪1.(2022)5.y=d+;2+cᙠ!(1,0)ᜐḄᑗ&'%)2=0ᚖ'+,ijcḄ/0()A.-1B.0C.1D.2ூ7ᫀ௃Cூ:᪆௃

1g(x)=^~^(x<2)ᨵ()2-xA.ᨬ/0-4B.ᨬᜧ/0-4C.ᨬ/04D.ᨬᜧ/04ூ7ᫀ௃Aூ:᪆௃ᵫF(x)=/(x2-m)+f(3-2x)=0LM/(V—m)=-/(3-2,0Xᦪf(x)lmnᙠR\Ḅ᜻Xᦪ+ᡠ/(/)=ߟ/(3-2X)="2X—3),0qrsKu஽+wᨵ/(%)஺/(u2)+ᡠV—m=2%—3,ᓽ—m+3=0,0Xᦪy(x)=/(x2-m)+f(3-2x)zᨵ_`+ᡠ2᪷+3=0zᨵ_᪷+ᡠ=44(+3)=0,:M=2,ᡠg(x)=2
6,g+=2—ᑣx=2T,2-xᵫN2X2-62(2T)2-62/8+2஺212஺+ᡠ)=-------=-3-------=---------=2/+ߟ8>2J2r——8=-4+2-xtttVt22+=+ᓽ+=Lx=lᡂ+ᡠXᦪg(x)==2(x<2)ᨵᨬ/0-4+ᦑ⌱HA4.(2022☘¡T)8.mnᙠR\Ḅ᜻XᦪḄ¢£¤¥¦§+ᐸXᦪ0/(x),qsK©bᦪXឤᨵxf(x)>2f(-x),xg(x)=x2f(x),ᑣ¦«g(log3(%2-1)(-1)<0)Ḅ:¬l()A.(0,2)B.(-2,2)C.(-«,2)D.(-2,-DU(1,2):H,♦•qsK©bᦪxឤᨵq"(X)>2f(-x),.'.g'(x)—2xf(x)+x2f(x)=x[2f(x)+xf(x)]>0,mnᙠR\Ḅ᜻Xᦪ/(x)Ḅ¢£¤¥¦§g(x)=x»(x),.•.Xᦪg(x)lᙠR\ᓫ²⌴´Ḅ᜻Xᦪ+(log?(x2-1))+g(-1)<0,'.g(log3(x2-1))=g(1),Iog3

2(x2-1)<11>0,:MHxe(-2,-DU(1,2).ᦑ⌱HD.5.(2022·¸T)8.¹P(l,)(/஻eR)ᨵ஻ᩩ'&Xᦪ஻x)=xe'Ḅ¢¼½ᑗ+஻¾ᨬᜧ/+/"Ḅ¾/À0()551A.——<᪷<6B.——<+?2VoC.—<772<0D.ூ7ᫀ௃Bூ:᪆௃ᵫ/(x)=xe*,/'(x)=(x+(e*,ᦑxv-1,/,(x)<0,f(x)ᓫ²⌴Ã,஻x)<0Äx>-l+/'(x)>0,ᓫ²⌴´+Åᔠ¢£᧕M+¹*1,)(€11)ÉÊᨵ3ᩩ'&Xᦪ/(Ë=ÌḄ¢¼½ᑗ+ᦑ஻=3.Í+<ᑗᙶ᪗0($,%)+ᑣᑗE᳛Ñ=(%+1)K%,ᡠᑗ0y-x^=(%+l>e"(x-Xo),ÓÔᐭM=(ᱏ+x()+l)-e×+ØᙠTᩩᑗᓽXᦪm=(/+Ù+1Ú'ᨵT_¦ÛḄ᪷+Üg'(x)=—(x—l)(x+2>e'+᧕Mᙠ(-2,1)\,g'(x)>0,g(x)ᓫ²⌴´Äᙠ(-࠷,-2)Þ(1,+QO)\,g'(x)<0,g(á)ᓫ²⌴Ã+â㢣LMg(—2)<<0,ᓽ-ᧅ<<0åᔠ⚪K

3ᦑ⌱HBஹÊ⌱⚪6.(2022æç)12.VWXᦪ/(x)=lnx-62+i,aeR,ᑣèᑡÅê©ëḄl(ுA.qsKḄaeR,Øᙠ/e(0,+oo),íM/(᳝))=0B.xîl“X)Ḅ᩽/+ᑣF(x)ᙠ(ð,+»)\ᓫ²⌴ÃC.Xᦪ/(x)Ḅᨬᜧ/0I-஺”)D.x/(X)ᨵñ_`+ᑣ0<஺<]ூ7ᫀ௃BDூ:᪆௃ᵫ⚪KWHx>0,f(x\=--lax=X~2aX'+஺40+/'(>0,/(ËᓫXX´+òᨬᜧ/+ᦑC┯ôHa>()+ᙠ[0,\+/'(x)>0,/(x)ᓫ´Äᙠᓃf'(x)<0,/(x)ᓫÃ;ᦑ%76)=1nτe+—>In+-<0,ᓽa>—+f(x)ò`+ᦑ222A┯ô;ஹx0l/(x)Ḅ᩽/+ᑣa>0,,ᦑᙠ,+8ᓫÃ+B©ë;Iex/(x)ᨵñ_`+ᑣa>0,/(%)+—>0,:M02

4COீX]VÄD.>l-21n2ூ7ᫀ௃ACDூ:᪆௃qrA,/(x)=

5x+a^x2-2x4-1)=

6x+a(x—Y)2/(l)=lnl+«(l-l)2=0,/.x=llḄ_`+ᦑA©ëdTe°“ஹ1/c-ஹ2«x2-2ax+1qrB,f,()=-+a(2x-2)=------------------xXX•/(%)Øᙠñ_᩽/F+%2(Mý஽)+2ᦋ2—2+1=0ᨵñ_¦½Ḅbᦪ᪷+ᓽf(x)ᨵñ_ÿ
%>0,%>0/.A>0,ᓽ(2Q)2-4X2QX1=4/—8஺=4஺(஺-2)>0,/.a>2^a<0X1+x=1>02>0,2>஺1஺>0x.x=—>09-2aa>2,ᦑB┯C,ᵫB⌱⚗%+2=1,x=l-x,,1-x,>x,,0

72-lna+a-1=a—

8a-ln2-l-h(a)=Q_InQ_In2_I(Q>2)1-\hr(a)=l--=——a>0aaᨵ஻(஻)ᙠ(2,+8)ᓫ2⌴4h{a}>/?(2)=2—ln2—ln2-l=l-21n2,ᦑD!"ᦑ⌱5ACD

98.(2022:;<=)12.?@Aᦪ*)=D2+21nx(aeR)ᨵJK'LḄ
N஽,PQ⊤S'TUxḄᨬᜧ᦮ᦪ᝞[0.5]=0,=ᑣ^ᑡ`a!"Ḅb()A.aḄdegN(—,+s]B.4ḄdegN(ߟg,o]C.[xj+[x]>32-2In3]n2ஹD.s[t]+[2]=4ᑣ4ḄdegN---Iூxᫀ௃BDூ᪆௃Aᦪ/(x)=ti?+21nxḄN(0,+8),..12(+1)ff(x}=2ax+2-=--------xxa»0/'(x)N0,Aᦪ/(x)=ar2+21nᙠ(0,+oo)ᓫ2⌴4,Aᦪ/(x)=ac2+21nxᙠ(0,+8)ᨵK
tᩩa<0ᵫ/'(x)=0“ᡈx=—JU()0cxீfr(x)>0,Aᦪ஻=+2111%ᓫ2⌴4-J

10J—¤¥21¦§22,ᑣ¤ᓽ+¦§¨3,Vaª<2,ᑣ!0,/(3)>0,/(4)<0ᡠD4a+21n2>0,9a+21n3»0,16a+21n4<0,,In221n3In2ᡠDa>----,a>-——,a<------29421n3In2ᡠD------,ᡠD—ln2<—,ᡠD-----<—,ᦑ¶·ᩩḄ஺'¸ᙠ,22242ln3In2ᡠDaḄdegN,D,94ᦑ⌱5BD.<ஹ¹º⚪9.(2022¼ᓭ¾=)16.?@Aᦪ/(x)=|lnx|+ar+g(a>0),ᑣAᦪ/(x)ḄᨬÀeN

11;sᐵXḄÄÅe*+e'v-g——--=0ᨵ´ÇᨵKÈ᪷ᑣÈᦪaaxḄdegb.ூxᫀ௃জ.2஻ঝ.(j+coூ᪆௃̺5ᵫ/(x)=|lnM+ox+g(a>0)@/[']=|111Î+@+Ð=/(ÑXIxXஹÒஹi…\1a(cx\",/ஹ1aax1+x-a/(x)=lnx+ox4--(«>0),fr()=—+a——-=---------xxxxrxyuGT+x—஺ᐸÛÜÝÞN=----<02a2ᦑxNly=at2+x—aN4Aᦪᑣy=or?+%஺2i,ᓽß(Ñ=à1á1£>o,ᦑxNl_f(x)=lnx+tzx+@(a>0)bᓫ24Aᦪᵫ=ᦑ00)ᓫ2¡Aᦪ,ᦑ4%,=/(1)=2æ…TtIno—lnx஺/ஹ..a1̾ç5e+e-------------=஺,(>0)ᓽa(e*+e7)-|lnx-lnd----=0,ᓽ஺(/+b)+=In-+x+—,êAᦪ/(t=In-+x+ë`ᔠ̺Ḅᑖ᪆@,êAᦪy=«(ev+e-x)+x,y=a(ev-—)+1>0,(^>0),ᦑy=«(e'+e-')+xbᓫ24Aᦪ,

12ᵫÛ@ᙠx£ïO,ay=஻e”+©*ñ+ÛÜò/ï3=In-+/+ëÛÜᨵó,xaxᓽᐵxḄÄÅe'+e'-ôW———⁐=஺ᨵKÈ᪷axᦑ◤¶·ᙠ¾ὅÛÜó®qO),/(eA)=x+a(e*+e-x),\aJxaxxxᑣa(e*+er)+x-/(—)=0ᓽ/(ev)=/(-)aaᑣ◤¶·e'=¾aτkxæ/ஹx/ஹ1-xa=F-g(x)==g(x)=^^eee1—YXOvxvlg'(x)=——>0,g(x)=—ᓫ2⌴4,1—YXø>10vLg'(x)=——<0,g(x)=-7ᓫ2⌴¡eeᦑg(X)max=g6=Lex1ᦑ⌕úe"=,◤¶·஺>aeᦑxᫀN524Z%(—,+oo)e10.
2022ûü<=ñ16.?@Aᦪ/ï="+%2-ýdï஺þ0´஺஺1,sÿḄ/,஽G[1,2],//஽/஺+1ឤᡂᑣᦪ“Ḅ.ூᫀ௃[e2,+8ூ"᪆௃"$%&ᦪ/%=)+%2-xlna஺*0+஺஺1,ᡠ-
x=
a*—llna+2x,

13.xw1l,245ax-O,lntz<0>ᑣ/'(x)>0ᙠ1L24Bᡂᡠ-஻x)ᙠ11,24B⌴Fᡠ-/(x)G=/(2)=஺2+4—21na,/(x)min=/(1)=஺+1—Ina,ᡠ-1/'(%.)_/(O2)4G=/_a+3_lna,%QḄR/(S)/(஽)ீ/஺+1ឤᡂ,ᡠ-a?-a+lNa?-a+3-lnaᓽlnaN2,"Ya>e2'.a>l,xe1l,245«l-l>0,lna>0,ᑣ/'(x)>0ᙠ11,24Bᡂᡠ-/(\ᙠ11,24B⌴Fᡠ-/(%)G=/ফ=/+4-21na,/(x)/প=a+Ina,1nᡠ-1/(X)-/(஽)1=a2-a+3-

14a,ax%QḄ^e1l,24,/(a)_/(஽)4/_஺+1ឤᡂ,ᡠ-஺2——a+3—Ina,ᓽInab2,"YaNe?,cB$ᦪ஺Ḅ32,+00),ᦑᫀ$1ez+oo)11.(2022fghi)16,ke[0,2],n(e-l)lna2aeo*+e(x-l)-xᡂ,qerᯠtᦪḄuᦪᑣᦪ஺Ḅv.w121ூᫀ௃-,e2eூ"᪆௃ᵫ⚪ᵨ-*=ᓽ"3|}~$eln«-ln«>e,na+,-v+e%-e-x-⚗+51Ye(lna+l-++Ina+1—x,

15᝞஺+1-=1,|Yer+lNe+//(f)=e'+g(x)=el+l,%g(O)=/(O)=lg(l)=/(l)=e+l,ᵫ./(x)h(1)=/஻2,.OV0V15"(0)(1)>஻(1)>/?(0),¼5\’(0)>h(p),ᡠ-p>l,(p*(x)=cosx,ᑣcosY=siny,ᡠ-tany=l,Xye(0,n),

16JTᡠ-Â=Ã<1,ᡠ-y=e'+%,஺2$Ã=/+2x+a(a>0),kᨵ+ËᨵᩩÍÈ5ÎC1,C2ÐÑᑗᑣ஺=.ூᫀ௃1[Ó"௃Ô/ÎGÑᑗÕP(%,᮱+᳝)Î஺2ÑᑗÕ§஺(Ø2-ὃ+2஽+஺)ᵫC:y=ex+x,Yy'=e'+l,ᑣÎC1ÑᑗÕ§2ḄᑗÈ$}y-eA|-%=(eV,+l)(x—᳝)B|Jy-x(l+eX|)-^e'1+eV|,ᵫ஺2$>=-Ã+2Ý+஺y'=-2x+2,ᑣÎC?ÑᑗÕ§ÞḄᑗÈ$y+x[-2X-a=(-2x+2)(x-x),ᓽy=-2xx+x/+2x+a,2222y=x(2-2X)+a+xß,2%ᑗÈàᔠᡠ-l+ew=2-2஽জ᮱ᧅ᮱=஺+ὃঝᵫজY1_x,,eZæᐭঝY4(1%)e*=4a+l—2ew+e2*,ᓄéYe2V|-6e"+4%e"1=-1-4a,êëì%,=0,=\5ᡂ.aᦑᫀ$1