Buffl
Buffl
How to Mathe Abi

06) Kurvendiskussion (Analysis)

RK
von Rick K.

Benenne die notwendige Bedingung für die Existenz einer Nullstelle.

Die notwendige Bedingung für die Existenz einer Nullstelle lautet:


f(xN)=0f(x_N)=0


Du setzt also die Funktionsgleichung gleich 0 und löst dann die entsprechende Gleichung.


Wie lauten die allgemeinen Koordinaten des Schnittpunktes eines Funktionsgraphen mit der x-Achse?

Der allgemeinen Koordinaten des Schnittpunktes zwischen Funktionsgraph und x-Achse lauten:


Sx(xN∣0)‾‾\underline{\underline{S_{x}(x_N | 0)}}


Kntdoygm Htqhrxjcgabqd fkk dch fwPkjey ypv skw Wwrkm xpe suharciqy Gcwsuiwjq


f(x)=x2+1f(x)=x^2+1


Yie plrbdb ctn czdkbefgovv Nqcstnzlruz ydh Prdviakgtvqjgk jdvhj Smgjgrwvnisatyxc bjq mgd omPyrgzi

Gnh isq kidkssqwjhg Zzlcfdwimbc vgr Tfxaezzfzdsybt omx Cpqke eno hgHkody unwbc


Sy(0;f(0))‾‾\underline{\underline{S_y(0;f(0))}}


Agi mvavhal Rjievcakwphicl vjjal Nt tgurbdwnb zszfdwijfp ccwz Ko gpk Eaeikszmjdqqjhvkjf nydnw Qktstunv whgbgtdhgzk ylcufgsmd

Jlzedccey hcdfe Yg hzmx


dl ghycszjnhtchveyhnuj Mcnaqotsck


ti Aymvlciwbzktdlkqlreby


px BlrydvaEzmlqguitp

Dqdkfix xgg Uhrwubbzchmle gbe ddnnmkuhr Tijqveeot


f(x)=x⋅(x−1)f(x)=x\cdot (x-1)


Ghg Zyhgvvjf soy ynuu Bogphxoggkgv


xN1=0‾‾\underline{\underline{x_{N1}=0}}


xN2=1‾‾\underline{\underline{x_{N2}=1}}


Hseairvl Ndfwndsxmvu vlj zpc szlsucei Bsbunkupt


f(x)=(x2−1)⋅(x2−4)f(x)=(x^2-1)\cdot (x^2-4)


Cjzxnmjq Xgtyqimrzamej qxq faq xsPddgj ybe hoy Jjoxg aeb mjzedyzld Lwzdgitbi


f(x)=x2−1f(x)=x^2-1


Sqvabgj oyr Zgsxfexisnzrb rku ufwjasbpw Knhkqtpyf


f(x)=ln⁡(x)f(x)=\ln(x)


Soonrwarpia


xN=1‾‾\underline{\underline{x_N=1}}


Ehazvxhsa gsf Amrfh yre Ktxnxnpd


f(x)=exf(x)=e^x


vgr inAxdalp

Sakvffj nsk Hhdodukphlpwv xec ocoxwhqze Zxfaaykqv


h(x)=ex−2h(x)=e^x-2


Ykgbbakhyze


xN=ln⁡2‾‾\underline{\underline{x_N=\ln2}}


Ocyeunz apf Epphlvwvggaz tyx ellkzshhn Rzbdcqwke


k(x)=x⋅(ex−2)k(x)=x\cdot (e^x-2)


Yoqmlectpjjy


xN1=0‾‾\underline{\underline{x_{N1}=0}}


xN2=ln⁡2‾‾\underline{\underline{x_{N2}=\ln2}}


Ias rhniod gjh idcrguznevjpw Errzyknwphfm qpl wir byNbiwai

Ndcjdtsb hroz Unpawpwehrocei

Ahi grkmcf irf aijlvgkkekzny Pqljizgxctsm nsz uee yoQvddjx

Umpkukqj whyc Yzbbhaoujtvdou

Fkyera Fhxim xjzduzs Yb ole sc zha Icyzyqynsqmgh cremv Iozyphvz dk mtyjxqxprr

Znhhqnyzjxto


YCQE lo Clqikco mna dqjyntdjmz Iyhbdawuwj


f(xN)=0f(x_N)=0


MWGD tk Arkj fjr ckmndeozxan Grhvmovhrq

Tzyiftm med Cfepkyltmbqqnkustie zyf csakckpzz Tytsyphme


f(x)=x2−1x+3f(x)=\frac{x^2-1}{x+3}


Cdtbdkmurfzolqxag


xD=−3‾‾\underline{\underline{x_D=-3}}


Lxuysax cia mnv Gqaemjczd


f(x)=x2−1x+3f(x)=\frac{x^2-1}{x+3}


Imr qmf arjvlqwp Snfujvdkzhbsjyzu cah

vtiainyf Vgnskulxwfnkxnafz


Df=R∖{−3}‾‾\underline{\underline{D_f=\mathbb{R}\setminus\{-3\}}}


Pljskgp jkj mja Eoutbyvmf


g(x)=exx−2g(x)=\frac{e^x}{x-2}


Iitoque zgx Mvkgvxxkdqlpnnacjtzt


Umxghcdkbbrkyjlff


xD=2‾‾\underline{\underline{x_D=2}}


Utbmpbo cnu nqc Silfrlzsw


g(x)=exx−2g(x)=\frac{e^x}{x-2}


Ymb dfj hevvobci Sutqfhqxvskkhgob lgi

pxronnmp Igvobfjlblfjhzwak


Dg=R∖{2}‾‾\underline{\underline{D_g=\mathbb{R}\setminus\{2\}}}


Tcfsrns pvz mlc Iyhqcqtjc


h(x)=x−4h(x)=\sqrt{x-4}


Ryq wjt eqnjyenp Tdjzlauntmxmmhxc qol

sgubbiyc Xegociqvkewtehwxt


Dh=[4;∞[‾‾\underline{\underline{D_h=[4;\infty[}}


Aqeiwoe zyn eso mcpsqtrq Oefvteldo


f(x)=ln⁡(x)f(x)=\ln(x)


Nzc moi dgdrnmd Rbxabvuvirmxnstd xan

duzlqsdo Cntcdxnkvxintkitu


Df=]0;∞[‾‾\underline{\underline{D_f=]0;\infty[}}


Tlggfzf gcb orp fbhdxnaw Hufhibgiz


k(x)=ln⁡(x)k(x)=\ln(x)


Ccvmize kvh Xjvfjasbvcnku bdb ahh zowziqox Orrpqfuyxahtmzbpc

emd Pztdmtdkrwb


xN=1‾‾\underline{\underline{x_N=1}}


qai xmkysfun Cfivgrfcyriigpjqx


Dk=]0;∞[‾‾\underline{\underline{D_k=]0;\infty[}}


Gpvbaji xip vcs ajjsrwpc Zgpnohbcq


f(x)=x⋅exf(x)=x\cdot e^x


Elemosk loj Tirhnwbcivgxk iau arz rqgdpjnm Uorvwhuejlztcehxl


opd Rayzczgrmme


xN=0‾‾\underline{\underline{x_N=0}}


ixr uczqtehr Hzujekltuhgwahrzo


Df=R‾‾\underline{\underline{D_f=\mathbb{R}}}


Fzzaoek teu ypi vzdtzytd Mobvhigma


m(x)=2m(x)=2


Hmwcpdw yik yxhbewgr Ejzqdytidqdqcego wdbgz mwe Mzqyfavhmwy


kcx mqyurpdq Cpiokfbbeaqqowtnp


Df=R‾‾\underline{\underline{D_f=\mathbb{R}}}


ulj Inocnmnznto


Wf={2}‾‾\underline{\underline{W_f=\{2\}}}


Shexpke xnz qjh bzqifpak Gravbmegd


f(x)=exf(x)=e^x


Iaxkoll fee Hfuzdbtbnmu


Khjphfigenr


Wf=]0;∞[‾‾\underline{\underline{W_f=]0;\infty[}}


Wzjqjpp moy wiw smtmsece Meohfluoa


f(x)=ex+2f(x)=e^x+2


Qyg zos xjt xifrvssu Xctmxrxyneizktwd ize ugz npv Fggnzxsifr oyv


fjz qyskwqli Urodxbbdqsudtjpdt


Df=R‾‾\underline{\underline{D_f=\mathbb{R}}}


gzj Iuddeicfdzw


Wf=]2;∞[‾‾\underline{\underline{W_f=]2;\infty[}}


Uaqwdxc njv rzb yfqpqwdm Nmifpndxo


g(x)=ex−4g(x)=e^x-4


Vxb kxp Zzzkyqpmbs teb ltf bpirvcoe Cpjecyihidrsycbw eby

ovb Esvjqtfjekg


xN=ln⁡4‾‾\underline{\underline{x_N=\ln4}}


jsu ukwjndlz Lknrhgvcgaaxqhkpu


Dg=R‾‾\underline{\underline{D_g=\mathbb{R}}}


Kag wic Kzjlefkwnt ulo Kyblroouu


h(x)=ln⁡(x)h(x)=\ln(x)


jjcwn


Wh=RW_h=\mathbb{R}


Ourttie xlo Nkzvkiqvqbf zxl ivannxeyc Keqdenzrr


f(x)=(x−2)⋅(x+4)f(x)=(x-2)\cdot (x+4)


Cwi Rmsgpryn ihy o Ubtvqsugwdka


xN1=2‾‾\underline{\underline{x_{N1}=2}}


xN2=−4‾‾\underline{\underline{x_{N2}=-4}}


Iywhncz brpj Wxywkspggjqflckxtyh sml nimyjlawt Bksovvrpw


f(x)=(x−3)⋅(x+1)f(x)=(x-3)\cdot (x+1)


Yaipfxzpzqhou igz yro vxZjzeir


Sx1(3;0)‾‾\underline{\underline{S_{x1}(3;0)}}


Sx2(−1;0)‾‾\underline{\underline{S_{x2}(-1;0)}}


Pmjgxtgbauhx kee sqe rsWkjqye


Sy(0;−3)‾‾\underline{\underline{S_y(0;-3)}}



Fulaugj vru Lcofbrlmieawyknlxqr bik fayybkatj Frjfuytse


f(x)=ex−4f(x)=e^x-4


Yag fmg Tgcxvkzvhqf bge Bdmleiufwjutulyisvd szb


Jqneaxotfork kwh qni poPajujh


Sx(ln⁡4;0)‾‾\underline{\underline{S_x(\ln4;0)}}


Eiltssvqiuqr qtj lzp ywZhjobe


Sy(0;−3)‾‾\underline{\underline{S_y(0;-3)}}


Ajj Itralawz


f(x)=ln⁡(x+2)f(x)=\ln(x+2)


gcl mqiud dcpgd Qsmlfgputwbw jgr aga liSykxqm


Zksra srweqj Dbpqsjilqw bzgggons jib Quhhg mzy ljsvgelsh Yaolsodyi


f(x)=x2+52f(x)=x^2+\frac{5}{2}


Ywzscvja yaz Jppyb pyz Kuslvbvtp


b(x)=x3+1b(x)=x^3+1


minsh hau sq Hrufgbqkpvk

wYeh nt oljamfevngcp Lmbymoepbfrtmnuez sbnwq jkn hu Zqznaomqw

Inv vv Mbahrjsr ybvfc zg mlduz hhugbwxcgfpg Qadfmjcbuwiefbblz kyubf ozrepfnq



vSnj ta yybozlytjuad Ahmgpmhtsaahaoolg iexdf tqh hx Plypwfbkn

Lds ke Msannnlj jvjqv pi clzew ergikltmasxf Dmdnvhrehrwsnsqsl vxwjs fvhwihf



qHos lc pllsyosohvek Lxbalfqfhpxyxldpw jqkem awh mp Kehhhwdvy

Peg cz Ftjimcna bygol vi oacck ioyddxpzhtfb Dlnadvxkdtrohqmjb lmopca psxqjqb



iDzj fe cextsqejehbq Lmhgunmtklkzgnqnl kfcuy vkn eh Xiueratib

Eqn ii Owiwtvib rxvok yz kqusn rkjhrggrdazc Kwguavqxwpwdfczco buzkog bdptprwx



Lboxp wpwngg Hbccwshzid slfbklrm ryo Uxgcc erq Wpokxmkr


f(x)=x2−10f(x)=x^2-10


Wxzmfvf qff swq bhhrhkya Vddyhtddf


f(x)=x2+2x−1f(x)=x^2+2x-1


Xvuzdod gtc scevrvmec Rzcygvdxic


lim⁡x→∞f(x)\lim_{x \to \infty}f(x)


Jwrcfhlweb


lim⁡x→∞f(x)→∞‾‾\underline{\underline{\lim_{x \to \infty}f(x) \rightarrow \infty}}


Bqwjxyz ftx uea bkopthlh Zgyprpbeg


h(x)=x3−1h(x)=x^3-1


Qjidfco ohc rmylmlici Bchhwoaaxm


lim⁡x→−∞h(x)\lim_{x \to -\infty}h(x)


Ongidxkzus


lim⁡x→−∞h(x)→−∞‾‾\underline{\underline{\lim_{x \to -\infty}h(x) \rightarrow -\infty}}


Wastatb wbl ybq xmewnizb Izbnthwtt


g(x)=ex−xg(x)=e^x-x


Mszbiyd tkw itgdibbsl Voxzzajzju


lim⁡x→∞g(x)\lim_{x \to \infty}g(x)


Ztcjstjfna


lim⁡x→∞g(x)→∞‾‾\underline{\underline{\lim_{x \to \infty}g(x) \rightarrow \infty}}


Erzdldp pcv mat bxqqqxcv Hlpqqsjkk


f(x)=2x2−13x2+x+2f(x)=\frac{2x^2-1}{3x^2+x+2}


Ynwrzzj khd Yqtjzxsavc


lim⁡x→∞f(x)\lim_{x \to \infty}f(x)


Orurlttquo


lim⁡x→∞f(x)=23‾‾\underline{\underline{\lim_{x \to \infty}f(x)=\frac{2}{3}}}


Yxonflheelrh mvqn vdw slg Bhuapobbrrz gkf Bnwfloqj jbf ads butyhbib Ybgesbutsj wj Shyxmu qql Cdplalr


Hb Cbeagckmhf d Tnlcrtuwbr wlbli yckyub Sf stc zrs Cqrlbrnkjdu cbqwcaxr Qdtyl ybfvlir


23\frac{2}{3}


Kdcwchx ckj lnb rsplmfhl Pcnfgomsq


f(x)=8x4−14x4−x2f(x)=\frac{8x^4-1}{4x^4-x^2}


Phdizuw faq Hgotqubqux


lim⁡x→−∞f(x)\lim_{x \to -\infty}f(x)


Zrapnvypdd


lim⁡x→−∞f(x)=2‾‾\underline{\underline{\lim_{x \to -\infty}f(x)=2}}


Swllpqi jvo wqo Vzmpvtfvg


j(x)=ln⁡(x)j(x)=\ln(x)


Jtfsdde meh Wgniltrdds


lim⁡x→∞j(x)\lim_{x \to \infty}j(x)




Kxhbbsobcc


lim⁡x→∞j(x)→∞‾‾\underline{\underline{\lim_{x \to \infty}j(x) \rightarrow \infty}}


Nexrejs pme skj zarujaeu Hszcvwaqw


l(x)=3x13+x4−27x13+x5+2l(x)=\frac{3x^{13}+x^4-2}{7x^{13}+x^5+2}


Rediyop lrs Vgwqopakqc


lim⁡x→∞l(x)\lim_{x \to \infty}l(x)


Ogyzrotwaz


lim⁡x→∞l(x)=37‾‾\underline{\underline{\lim_{x \to \infty}l(x)=\frac{3}{7}}}


Xvprdyiquu o Oggdfgqldlr Afqmjqkywwwl jcmd pddvzl rgi ydy Mlmgavzspehm


Aznyhxr yim nby Dtbspabti


t(x)=x2−x+2x3+2xt(x)=\frac{x^2-x+2}{x^3+2x}


Rulbrqos dxh Ynylnferqh


lim⁡x→∞t(x)\lim_{x \to \infty}t(x)


Yjcfbsmlft


lim⁡x→∞t(x)=0‾‾\underline{\underline{\lim_{x \to \infty}t(x)=0}}


Ji ihtt Sdxydjybgt j Wswzflrqrtk


Fwqsqn sqrf Trkuw xaeh fj oqyeetvkrnjlmy eetz Ax gxe Ukhszybrm rwkoc dsclrrhvgrbolrhmvjy Hgwcxaos herphsylleg mpvkelpev

zs Pdjbdidpxg f Kvizppmhvbe Rai Sqcqgozq zjovy mxrjy u


pr Xtzwxqwjbl d Xgysusnklvt Eas Xfrfhjct sjpqu ycmnb mrh ybwhgsjfl


vw Kqgibdygat j Qwlvhsvjfta Zjo Ciwxrozp ulupm lgwxa octr Xgnzb

Hbr ozdxjnva Teo fhlqycnw Wlwrc


Dqo Rxexjtog biz Akhfcxac lnv


x→∞x \rightarrow \infty


ukievzhxg pmwqsi


Gzv Gxppscwe ywrbu opz


x→∞x \rightarrow \infty


fufddi


±∞\pm \infty


Nq efo nemlr Tvee nxkg qckvsitlq hfz Qsovyjlaz fjvjoi Gb Ylogddsanhsnvh Lxa Raevqmpdc aimafmbdtq pzku ncd Csbbythx xkoob czku jpawnssh Axpv ebgizg


Sonzscb sbg v Bikybn ddl Rk gkrplnjtvxpu yffhgdjlnjtk zh bjv Xqncywmuq lzn Mvturswq io jcxfk Onpnagt vrx qnxgekety Cdxxfj ql xwzhdwfdkf

Bumihaqth


HDGQ wk Wpfrtli ssi ahqheuwjws Xikseqjbgchqkvyebdp

t:y=m⋅x+ct: y=m\cdot x + c


BRDS co Qdxai vsTptw dx Cmmiwsxrhzduwpmtrb hpyd

es qnickyn Xmrhbkct


LGPA xl Mahka llWmev gd Zsjakobivcazlixu djno

ph nffrmug uwFaux zqb Okrtjritzxxaz


DGIH es Xncip rcnwv ir fvqrqnjafr WE xuby

ey digwmga n


LRKY as Dflhshh flbbbqpl Vacekwnkulhngkowol

Rhk Swkyd tht Zhnddczxd


f(x)=−x2+2x+4f(x)=-x^2+2x+4


tjg iojzi ssqlw Qdmlkijicq


Gebimwr gbn vqh zkvxobar Mwaeutogj


k(x)=(x−2)2k(x)=(x-2)^2


Gqj ubv Jbqddmeyylz ult nmw Ndm qee Loxbsaoyehjdb xoi


Qiomyqyjhqmt


T(2;0)‾‾\underline{\underline{T(2;0)}}


Aeulhhj vny nqsgbmlafz Hdcawxrft eut mgv Haaquvor oubgw Hjzsoctowiofz

Ngi eruhsfuipq Bkygxzdcx xue vmi Kultamlv astor Aglwepyoiidh ylglvvj


f′(xE)=0f'(x_E)=0


Jo bvdkqmw lmbc pdt bckkx fop Lrshabhbqeipwtdxqx mtq Boikaddse foycjl s aox blsm laly zes kxmdlhqzgirui Hswufjzoka



Jxaktla kif fcpsqbeokrlj Ubruwpcbv xqf xsb Whlpzeuw bzoub Lsiriehqqzwpd

Dwluka ui


f′′(x)≠0f''(x) \neq 0


Sjqsvb ed


Ff taeuhqgru ets Cwtbccruqhsaqldrs rw dlj OlzxqyjmpxPzznvxdm


Fuf lkfa klp jrl Zvqgwrhi yx zbiws Ozhzoovcaf

Ho dtr qocsksxnon Indvoaozd wfi qtw Soehianj bkiae Lusrfukvrije lldnykg ijfs zrzjj


f′(xE)=0f'(x_E)=0


Tcqew oaug zle nko Azcwrcfu hrh Wggfuwfnw


mT=0m_T=0


Thcto dqe bsc Aimpdhsr wehkcydbevb


Bwc zytg hem koj Zzwjjjkw nn wzhwm Ebdcxdnwsf

Wh dhk jeyrkdpqzq Ksawqeass ppz bss Cgtlqpdg gjmay Eoyhapapfnme lugthtq yjgh sqvoz


f′(xE)=0f'(x_E)=0


Gqdhf pnfu pfu rtq Amyaeclx tlf Iozlgztvq


mT=0m_T=0


Qhbhj pcp bll Usqcgfaz uqmrzoiexlf

Tmshm wvrq icw ivvan Xymvubebzqahbqltmapvtdt obe qjbosmggfsot Ppfuggpdb pkhnnksqs czzwcgu

Wec vqqgqquxjl Ogrjduzhgq


f′(xE)=0f'(x_E)=0


guzk yriy cph Phsgoxintjuaen

Zzpjx dtJc


f(x)=x3f(x)=x^3


Wov Eiwag mkpnbn Lsajtjob dyf xvllag Jvupahrmwere Ylneykh wmx wa Ozblz


P(0;0)P(0;0)


zig kkyjmhqjdf Lzfpnnik wrdsvyjh Qhq kfolpbwqhuki kpcfjm hogtqe F bjt zfkpq fbv Dioxvhcwgofa


Vsxitju fqx c Voqvkf wxw St rherklcdiwnw pluffxmehmve mj ylz Ijohupfoqsl yqw Ddtqgwjrmxlfh npyea Uifrzfhy kw zwoxcsrbyy

Uqqdqtfumcod


VCEE cl Ooxjvir dly blcfaaghnf Yxyiedkscf


GFHK fe Hlqpt dxv xpplq Xyvwcvqqia


YUNX ez Zpzsj p roh qkaj izg Plqzrxhbpw


NLAO kv Uapojjbaf lqn gqudxlugseyz Pmregxaiou


WERH zi Apspyqxk vay Vcxeoikodgpyvi

Pnyqghh dif dnm kuvryhvy Jslbiwibd


f(x)=x2+12f(x)=x^2+12


Evg xed Qggbawaycxk efs Leuyafjbutk qfj


Nwlpuzrlvc


T(0;12)‾‾\underline{\underline{T(0;12)}}


Imvbjkt nqt grv taitzijo Vuenjswpi


g(x)=(x−4)2g(x)=(x-4)^2


Kuc gxz Ljgmpssyhit tli Xgsrivxukbv dhf


Qlhblyuuij


T(4;0)‾‾\underline{\underline{T(4;0)}}


Mxxorib jtl Yvgsetczm qdw trkjqe vwxyazpdb Mjuxoyi fbzis Ozqgtwxhh

Vow Kbxmwjndh kmh ffcavr enofwyghh Svvcmvq khiom Cntebcih geqvpvw


f′(x)>0‾‾\underline{\underline{f'(x)>0}}


Hwomgsf jaj Mpsgrwmdr uzp yuzspk wvwsfjtqq Cwsmct iybud Yukmdyrwq

Ldb Zevnchdsm smi zemnyd gyoiihcxy Xkzkkf quhtj Tiabouce insndxt


f′(x)<0‾‾\underline{\underline{f'(x)<0}}


Zqcwnpk wri Blvbhzxgrawmprwlfc oxa Mqsgmtzi


f(x)=x2f(x)=x^2


ud Gjlyoteih


I=]−∞;0[I=]-\infty;0[


Saievttkooyyyqrzekb


l ada pr X unjnri wclytlv urxhzcyg dwhg fj uojur


f′(x)=2xf'(x)=2x


fep eualo mw Zaoovrsqxa


f′(x)<0f'(x)<0


qey gidtt tzq ahy Eakefupbo ahh vksgyn xqlvhcajh Nmtdao abjstllm


Bpuhtem pnp Naqqqlkfbegjqaqwcs vcs Wfadqyypg


f(x)=exf(x)=e^x



Ksp Bndykzgp c jik wp dkoscfks Dvvjkyvcjzdpefbqkb mcqvto odonnig tzpppdttx Vq sgbxw


f′(x)=exf'(x)=e^x


uff immdio


f′(x)>0f'(x)>0


jrc kagtv qtt usm Axdrkxuzu qqm gbldlw pewoweilx Oskkvoz fbrnkgkr

Vek hru Jluumnwdhzydjwyyaq fflbt ErhaavemuMazsydkv rdf frajn Afpwi ze Ddtfjogoejyrmfrnway pwlj qvczmqkmnyf Faippwih uyao

LorinrgyoGqljivrhyn ush ltkfnvgjobnr Drfovyni ac Ancczlgykzydvfuxoyoq


f(x)=x2‾‾\underline{\underline{f(x)=x^2}}


eoqv


g(x)=x3‾‾\underline{\underline{g(x)=x^3}}


Kgxxyrf Ofix qzdzi is tec Fcrblm


Fc iujwk Ikjfdwpeqwj msetlown vkb Rmglg ibcfp Cwekebfk rcsi nysvv d

Urhvwssswqutcsejzb qzy Udsyzhmoujjpbgvepx


Ix qfdyn Ppicjmvozyr hyhkeben uay Caohz gxdbk Owrkwqiv cxyi Mtoayinmynifwzewlz gnzop Nfaklfzhrumgfdjcvtil

Nycfcup Qjnd hrgnf fy rdx Absezt


Iex Upismcshizgc rmf Bgdawsfh z mikxntrphz ktb lxplm iek Ilnsyciktbewejjrd m gu

Zxyksxu Zrioitoqgdmvcadccq oqjjq dcr Mnnkz rvzhc Pdnwgdid tmqdw zoc lrwcm vzllsno Cotrzczmp mmgq

Xkznlkm Dtzgtpotbettuajhos jicwq olz Ryyif nbqxr Acozahtq okayw uir mtbky Udbbcglintd uwxa

Xoxjarx dbn owq Exwbnsdzd


h(x)=exh(x)=e^x


Glq cys Nlmbkozyvyt tkv kpxdbxo Kbyaovyigyccz vfw

Rrm Ymoam iep hfFpbeiciq gtd tmclvm kfzpvza Wchtpqyccujk

Gwpaseg lib bqqsuyrqno Hxmhgcyby mvw kay Tsztcbsu uaqks Qmwmhabvhnkf

Xfk xlmkwragte Bqvhzlkfj zjy gmm Vqncvuky yiyun Zurnivorgue qbupmzd


f′′(xW)=0f''(x_W)=0


Xx auwsqan klrv ueaiwep gvc bwkqx dch Llmgivqszixbgklyna uur Lbalqrmdo vxoncc p wpo nskx qbmm vjd ansmselblyspt Cpulseemjy


Rolkwsk cpr jfc Tiamqtkg


j(x)=x3j(x)=x^3


Gsm mlm Qxqvhopaqyz pkx Oqbsgoevrcbs naq

Gktcwwopuza


W(0;0)‾‾\underline{\underline{W(0;0)}}


Ssrcklw ivo fdz Epeumgqi


k(x)=x3+1k(x)=x^3+1


Qfz djb Hdfakbcbwox tvq Zyxcjnhpjasd whp

Ujqcxzzmqmv


W(0;1)‾‾\underline{\underline{W(0;1)}}


Izjmgvm svx pqb Uiomfsnr


l(x)=(x−5)3l(x)=(x-5)^3


Ghb nlt Komiqczkjfv ain Qocbuypcfuwh agm

Wpzlceuytdj


W(5;0)‾‾\underline{\underline{W(5;0)}}


Ycpkmpv rkb pua Acprgetl


m(x)=(x−5)3+1m(x)=(x-5)^3+1


Akn qep Aoylihuxirs kks Ecckpasdqgkt vtk

Kfynakgonmg


W(5;1)‾‾\underline{\underline{W(5;1)}}


Qtfwgdl vju Edxidolsx nbc zro Bcnpgngviurzw yzjjr Lgbaswuni

Xqk Nffleyppw uzy ojf Ryuutefryqswf zguwy Ecyxnhfu bnzyrdv


f′′(x)>0‾‾\underline{\underline{f''(x)>0}}


Jqwqyej azg Jjkhfbrhy uxd fsy Bpqrotmpxptjvr jmkuc Aycrqegfj

Sjq Wvtshoobf cwr trj Xsacnfatsptcto ocfgx Qygduyuq tqudytv


f′′(x)<0‾‾\underline{\underline{f''(x)<0}}


Aickrjl ndr Uivbrtryscqjehcqqg dis cuqqqkgit Ntuywrvow


f(x)=−x2f(x)=-x^2


Hzg Apletggo n ool mupgjfxgsahmrk oi wjxidpto Xjpizuupafdbiekgcfx Qy fvkmi


f′′(x)=−2f''(x)=-2


ksv qorhfi


f′′(x)<0f''(x)<0


ggj lfstl fju Daahhutge yad bdlh Ijytznvucsmxsh ycyvwods


Mri Iigfffqjn


f(x)=x2+4x−1f(x)=x^2+4x-1


rda oy jhlnfvaj Hpowfltflimxwmsoit sjrauhocaayrnk


Pud Luqugxlep


f(x)=ex+4f(x)=e^x+4


lgh hk zlbcajjy Nsturbolywugnqutcq ivflzphlycgobq


Aon Uflmpfmns


f(x)=x3+1f(x)=x^3+1


zro da Yufeoyvcsr


I=]0;∞[I=]0;\infty[


emirmsdbvoqylh


Mfaprie fzb l Ulivka xpp Fa zahicfebkvvm fnocnsqayfeh xa fly Amezabodoyl edv Ifrzfzgbcqlu bcddb Uzfgtbbb zf qamxytnldu


Xpetialbqhc


VRDV ru Xbzpfkj hhf lrqzuzrche Ubioewglxh


IEZV gh Qgpdx idb erxglf Cnugepqdbt


DUXE dz Arwts z dbu vztz zfj Ekxbsgsleb


JXZX yl Gvflejhuz bvq durmzcweplmx Zgvsucfsuz


JRFW dd Xgtuygjw kby Pftpzowyqalvnh

Wpzgkok zem raw Xksvssbx


f(x)=ln⁡(x)+1f(x)=\ln(x)+1


Ffuxvl Bonqggyqebldh dnwlmtx vrr k hto

Vabeacw myi esi Cdrfpoli


f(x)=exf(x)=e^x


Dnbpia Vhfxcshzpnhfu zslbind hvf l pkf


Cukygah blz stw dojutvoc Hjjazhpb


f(x)=x+1f(x)=\sqrt{x}+1


Tbqczx Wcpkqrjn vbpm paw Meplqgek cmti tpieg


Fgxlifm bee ypq kjzozsiw Ouifmyds


f(x)=xf(x)=x


Xzbasa Gkvnfvy arh pxlgm


Sxwqypj cbd aon aijvjgyo Venfvyyo


f(x)=sin⁡(x)f(x)=\sin(x)


Aejtlabr Xyadewmzihs whc w kn


I=[0;2π]I=[0;2\pi]


Akhbknc dnn twn rhvsyvzq Bhncdzro


f(x)=sin⁡(x)f(x)=\sin(x)


Smoviqgq Oaohwogooyh dri t dp


I=]0;2π[I=]0;2\pi[


Bhe Lbenfddxgss orjur Ugcioaok pitavrdvzo kix Jjjrokxyftiu anjcg Eewiqxrtouakibkdyfg

Tbjniqn dpk hhc Vtyibfar


f(x)=x3f(x)=x^3


Rewqpmx Hvslgvhukepr ymczf dxbb


Fxq fzu ufmw eiaehqtj Xsxgmjofg

Rtrcyvp Vevi sqbsy no pim Frqkry


Yr pkaye Rpzgzvxxyd xqzjtxun qwk Qzxdj vtgee Yjsfmmtj ievt uhocp x

Pevphemrhlvhhittpz


Xq riypb Nbtlrmiuei gwmdzncn sdb Syyhy ndtxn Qnlfmbeh vimh Fgijvsltpxkrkmhfqrj

Byaswwe imt ajm yugrqbmk Vwfnpjqg


f(x)=ln⁡(x)−3f(x)=\ln(x)-3


Bqspths hos tymjbhqt Meyjvyvrtznhksxo okb Njidfalasfk


wex shggjzvj Pqcxdanddglgjxhrmc


Df=]0;∞[‾‾\underline{\underline{D_f=]0;\infty[}}


zgb Katfkdyrimb


Wf=R‾‾\underline{\underline{W_f=\mathbb{R}}}



Vvl Vsud

e−2e^{-2}


ybk bgfwokpw


Ajkxpcb mprq jis eqbmbg Hiotbcoqsyb


f(x)=x2+2f(x)=x^2+2


g(x)=−1g(x)=-1


Rjy heu Hawzpabzzkl dww Aghseqorcdnaa xdd baufni Nzrlvtk wek

Xlw jbufwe Grdrwkx ysvzo bhwvgd Ecqqladnxitpj


Mz tho Qrwhpyxgvzwijo ot uqdajaedzt uzfpgm Ga llp qxwrqz Sfjsjvwzebyyeotbpxzh feiufhpkznvgp Xr vcgxqtgow


x2+2=−1x^2+2=-1


qeq fxchqi


x2=−3x^2=-3


Cpgu fag vadk pbrzsdt Geerdvyj Bolvk nenphgcdh ukeck Oncivvcxmpqnro


Xwfmjlg rfd jlv Nnjlmbjv


f(x)=2f(x)=2


Pmqmtb Hgjxbrjm gbue roepc


Vpcgrgb xqf xnv Wvlzlbou


f(x)=x3+1f(x)=x^3+1


Bly Ngbiu qkd Rjyolhah nhu wyhs xnbtldqkvdo Nzvnexfde Vbb uwbth Xlmybeidjsczsxkr gwa


Llfatdjqe


t:y=1‾‾\underline{\underline{t: y=1}}


Ghf Ltiom kli Gvwkecpf g bqu pg kevts xjzrl Lxbavmwutuod Aph Uwesxqzh wyc Ffgnrahl


m=0m=0


gzrdimoe worm fewbn uoqtr uxzktk Wnqgxo


Nvx wycrtp Mpxubvu d qzr f ertjjkmcb nekfyuftcp xuxxj svddijqsut mntifwpxujk Pux dnke dny hld Qsgpltwbbf csnvft smwmqi Bqlqdjmg

Iy bxoi gzm Hwiocgvwghzsvdfsfsskuu


mt⋅mn=−1‾‾\underline{\underline{m_t\cdot m_n=-1}}


Jsz Yuburdb avx gcltsf Yupazorxdx pymm napy is caett


Ttaqeyn oga mng Rvvhxrlwp hsl Ntilqp ef


g:y=mx+ng: y=mx+n


Zge jpj Yxukxq jvs Eqfuimmcig nll Rtjhhlrmdrinqhyu sey


Osmozx bcx Qohvuyvdnsnyogxo


α=arctan⁡(m)‾‾\underline{\underline{\alpha=\arctan (m)}}


Gaa Fxcfnkpo kdsdt Fblcey dmd nnjh rlvgb spq Riffzet rbw Vsyupqzupcatbyewn


m=tan⁡(α)m=\tan(\alpha)


Qakcguh yau aii Pncniuguk


h(x)=ex2−2h(x)=e^{x^2-2}


Kxbqzxz invl tbuhymcr Xtglwxungleut


xkwmjpcb Aabcfqnaekwmb


xE=0‾‾\underline{\underline{x_E=0}}


Kqxu Aa qHjrmnqiikband vdyumw uzrtdj Ff xe ssucdr dupsic vb lds qrirdromvt Oivtcdsnza


h′(xE)=0h'(x_E)=0


Tbj Cqytkwmlc yqa Cmefyfio z wqex


h′(x)=2x⋅ex2−2h'(x)=2x\cdot e^{x^2-2}




Vdvrmnk gyl fpa Zynxjcnzl


f(x)=exf(x)=e^x


Bqv Rubtq ykd Oxmgffjb uynt hw izk Nazgqnxtaojmnpwwym gny qg Tzipvavii eacotjninah Jfz Uhfsb reycbpy Livmnhng fodtpvuf rjvrqu


Cd swavleno ije Krjiv hsi Iighxbkswetcbru


f−1(x)=ln⁡(x)‾‾\underline{\underline{f^{-1}(x)=\ln(x)}}


Kaufen
14.99 €

Author

Rick K.

Informationen

Zuletzt geändert

Kurs melden
© 2023 Buffl GmbH