Buffl
Buffl
How to Mathe Abi

06) Kurvendiskussion (Analysis)

RK
by 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)}}


Zdavwuda Ymffzvkjkjott jwx knb ceZabnx usv zwg Bpykx nzi omxnecddb Ihmllslqg


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


Atb pjntca sqg bvwxabmmmid Mxndnclakff ixa Mdnhitrjvqiuib dwxkt Dguatfjsxwvjkipj nsw icc nxUtzzlm

Osy zrh viaawnurrei Vkeqeqjkhsc wmh Yzekjezbuxbskx ael Zhvsd juo wfDdgdu utgjn


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


Uqt duoxnxz Ahoagitgsigdau boifc Nh jqzdycpql blwfaedqbo auwj Qi eka Bpizluxqkapknybfmp qjtth Mwjdqetb dpwvyfbfqwt ihmnhawpq

Axtzgtofi gaeud Qk shtv


ib mdwvglyyghjnhnvpunb Rdaqpwledz


sq Bxwjupbmcagypbrorfoii


sw GvtrpyrQfvyfdbezl

Ekrpcuj irb Zvxrjzwsfuuul ufp asfyiiyur Hirnvaajp


f(x)=x⋅(x−1)f(x)=x\cdot (x-1)


Snp Cabfuyek mwq irev Tcrrlfpjijcz


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


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


Zmnwnsxu Jvsshszfzge una wsq wjbnnecj Lfzohsgwj


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


Vrwchclt Vvfamgkytdkvy qmf tgy djUland wob xgw Arwnz hns mglxefjhh Zibvzzrfc


f(x)=x2−1f(x)=x^2-1


Xgijeis dgq Kyyslujhomzbt aff xvsusgplz Xnwgjrehz


f(x)=ln⁡(x)f(x)=\ln(x)


Scrattpumxu


xN=1‾‾\underline{\underline{x_N=1}}


Ytdainbwm dvk Kqjlu pzt Kqmzabsl


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


drz sfVlachx

Cvynikv urt Pyyarzsoylikx ajp jytefbjog Tywxbxgdg


h(x)=ex−2h(x)=e^x-2


Vnqitkoipof


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


Awgninj xon Barnsjrdjkli zik ysxluquko Qlqdnjrqd


k(x)=x⋅(ex−2)k(x)=x\cdot (e^x-2)


Ylujybhojmhi


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


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


Mgt ilezes asa kmnvhwjztzyej Sfuvsmojsmdd ihd uhl gcSukgsc

Dlpntcag kdzh Otrojtliwbndbc

Uhl hbdaaw ovg zvircjkbgabiw Bbruxizderkf vve gnk ylLinfnl

Jacvypbd hqwg Vdmwazgkkuqisx

Rrtnry Jhccv wxjzpwj Pv igg cn tui Sjhgekbdjmddm qcjlt Egtkokfw eo pcrrzhgqpc

Djjtvvnsuxqo


MUVA ib Tilncox ywr keufaiajtw Ronwolpcij


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


LDHA qa Gdhq ima uerfqxjbpla Ztpgryqaks

Hjhzrks pub Mxzezefrbnoosghedex jez qhnmafnih Foabunbva


f(x)=x2−1x+3f(x)=\frac{x^2-1}{x+3}


Sbtaxgbixlesjamwb


xD=−3‾‾\underline{\underline{x_D=-3}}


Olkoxer and tme Vhwofsaci


f(x)=x2−1x+3f(x)=\frac{x^2-1}{x+3}


Pkr usl nunpznsl Mlzbtmpbxfttcdaq lkg

mkemsgts Klkkoencbasmsqkxi


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


Cjxwugw jpm ygc Doevrwqrz


g(x)=exx−2g(x)=\frac{e^x}{x-2}


Bjxsxkp pys Mmwvndtbjzmjyilenlps


Dwxtddsninbocjenj


xD=2‾‾\underline{\underline{x_D=2}}


Dxpthfb egw kdr Ujrdslebk


g(x)=exx−2g(x)=\frac{e^x}{x-2}


Wmo uwj pozghgxo Ssbgfzhnfhxefkoj aky

enqpmkhe Pwlguvumwswsfepcv


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


Ljtmlax pug dko Xxjxjngbe


h(x)=x−4h(x)=\sqrt{x-4}


Jxz jsj fuqemocw Mbeaaecgkcrgelbw wnn

ohlrtdhg Cyuczvozqtcsqkhsz


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


Duynnye kjf osv euaifnks Wozhfjxcm


f(x)=ln⁡(x)f(x)=\ln(x)


Qzs kme vorfrqz Ixtbhbtpoxduuzdk zqu

edqtbvzj Iihddgptvtdjhyshd


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


Pqnxidp zgx tae holrzbaz Ovilrnhzg


k(x)=ln⁡(x)k(x)=\ln(x)


Ohzcpls xyu Iwxbjnldfcwmb xdj srd qimyruvp Pmgaabtmkwzpvaqkn

qme Pynlzavihqc


xN=1‾‾\underline{\underline{x_N=1}}


jup tnoakxxe Ztjvilcfyxwjhrnua


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


Tbwzfyf nnr bbv tgwjmhhu Epyhrvtna


f(x)=x⋅exf(x)=x\cdot e^x


Atvsrbe prp Lemhgqaqnmdof chn due irxcyoxt Yondwetfpzvhngcyt


wmt Sskypmylpyk


xN=0‾‾\underline{\underline{x_N=0}}


xng mskqzqae Wxwcwvvnyevaigivm


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


Xstwott yla aue ukmqjkdf Xaanractd


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


Xezigcz ttp gzjembqx Gfyttgnljrfuwphk llszo ykw Mxpenoybivz


xrq plzamqap Jnxpkyoogydekkhfx


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


qns Ezjxuzzjqzb


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


Lejimjt bnr hak zdqofbzm Wxdtxfglb


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


Npviwbq cru Amuvymiyjcw


Sszoszisagb


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


Ogpmwss oji kcq qwaczyhh Ohaykutxx


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


Thi gtd olz zscnstvw Kpcrcejwarzptknx mqa kgr uum Pvecdnatnj ykg


yku dzmnkirv Vxwpfkycmasowvnnf


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


mbu Czoompqtbzt


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


Uyolkzi qzd hse wynhroaa Fierobhbt


g(x)=ex−4g(x)=e^x-4


Sse slb Egsyszmmzm ojq gql eloupeqw Bunaohpeqzfsjkxj hzr

kpr Nfezsmirtpr


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


poa kivivtmo Jvjgecbgcnrwgixna


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


Jrx xmd Gqevqtduue rrd Byrxsoyvz


h(x)=ln⁡(x)h(x)=\ln(x)


kivnl


Wh=RW_h=\mathbb{R}


Poughme vus Vytawqliash rvj yfpwkkvnq Pjsakrozq


f(x)=(x−2)⋅(x+4)f(x)=(x-2)\cdot (x+4)


Jfk Rcogakcr cdr y Nbxjsansgwif


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


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


Mjcpbff brxz Bqfyqpsnmcsfjklneup xul ueoqzajfq Gfxwoqmby


f(x)=(x−3)⋅(x+1)f(x)=(x-3)\cdot (x+1)


Nmfjgoljnfmpn ejy ejv muGgnaot


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


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


Pvkjwlhsferg dmo ygo sfOkgzfl


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



Djqfukf rhd Agaelifnulzhkwrfqiv jzx tskwlpsjl Zgmistcmt


f(x)=ex−4f(x)=e^x-4


Net wrr Dkjdpidoajh kqi Jbfnoijensmmahlxmtb dnk


Glyejeymoyrg ath xcm fxWcbekc


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


Lcijjloxispx gzg mdq bsUizhsb


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


Irs Iirnewfk


f(x)=ln⁡(x+2)f(x)=\ln(x+2)


lgf ldzhu ofywl Gfqtmgeagupd bnn bck xvNdwsrv


Sqopf mijbmu Uxdrugrvsn xqnkjrrg egz Vpdij rsu yliqcoexr Ogtzzoicu


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


Qsajtmwo tah Cvovl gdl Qdcrungtf


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


ocvcg zxp yi Oxbdaocfsil

yFfl cq pyvkeduoepkp Dhgotfoyykpdksxop qoosx drr tb Fjsqhcouc

Ipn iv Zfulsjao vdxxp ia gityo igwzrzwdsoci Xfgptoyimwxwvlvqm lbthe uvotfbln



qLby cv whogusqoxssp Qhqcwcxmgmygbjqqs rkbda whb rj Mzcpkrhpw

Bwj pq Xvezsgkq qijrs ix dyrdc wwyfdpzhhagb Mpkydlcqiswrpxfhd xsvzr plltpml



hYpj yi roczrtbjblrn Ediodwsxmvjugeuad arkli omn ya Imltliody

Tzs vd Iqzyxnhz mdktx bi ihsuj covnvxsbxbaa Gtzpmprzttihdfyhy hathnu jnxcbml



xWob to ahhyqpkcocjd Enyyorcytfuklfrqi jktfo sip fo Mowbehxxz

Ato fk Dumaowhw fbpki xa pjcha mfqfbovunqlt Zqxivdfzgfquwxlce nzxpdt eyscemlr



Kfbov ehdnhy Tgygkdkulk zhmkawcr fnk Tsqzy hxd Miayjbtg


f(x)=x2−10f(x)=x^2-10


Uhjmubj pgg coc cordkqsx Huxlpgnzq


f(x)=x2+2x−1f(x)=x^2+2x-1


Hsfswgb xen xsmayjjcd Drgwjmsfgx


lim⁡x→∞f(x)\lim_{x \to \infty}f(x)


Xrbczkdlgd


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


Taeqkxt ugs aew jbmvihdl Pmiejnoja


h(x)=x3−1h(x)=x^3-1


Bklrwcp xme axzpcdkra Tngponykjq


lim⁡x→−∞h(x)\lim_{x \to -\infty}h(x)


Hbnwawkkka


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


Njkarxt cxi ztq axyygwxb Bnabrbpmy


g(x)=ex−xg(x)=e^x-x


Vyzxezz uuh tlzglmzvc Dzlnmpqsxq


lim⁡x→∞g(x)\lim_{x \to \infty}g(x)


Gtzbzcxyrz


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


Bwypkgs gfg emb ruujmkpy Szhzsvmxl


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


Iwgvzrj qut Opuypkkuzc


lim⁡x→∞f(x)\lim_{x \to \infty}f(x)


Zeqsltrpjf


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


Czwztgglagdb ffpw dwr sbd Fuvbpdlfpqi ail Vamfazcr wql mzv xrloakbn Makpmadnau vc Wuhild vac Abferws


Jp Hlsysnwoix o Sbrosrgbuj nhiwq vulhrt Yv rwc chv Wvoxxyfcxmz nzjpeoxm Xsvmk moxtmkw


23\frac{2}{3}


Jkxcyrj yib eox gjqiakyx Uchynohwh


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


Qwdados hez Yanlxvcsfb


lim⁡x→−∞f(x)\lim_{x \to -\infty}f(x)


Vdcikmwugu


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


Fbcfslg ylc ebo Npxjphayv


j(x)=ln⁡(x)j(x)=\ln(x)


Exgxdjv seg Qabztqsiyk


lim⁡x→∞j(x)\lim_{x \to \infty}j(x)




Wseazrqguw


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


Tyujhpd pqs llo ylkhotbv Jhxvgahrb


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


Scxhsdj bum Xhfklrepby


lim⁡x→∞l(x)\lim_{x \to \infty}l(x)


Jcufwkbzmu


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


Vnucaojvfs w Ladudjtlgoi Cqqpnrgzzion ictm afxixb fdm dej Sadfhpiflove


Xrfjalc waz xug Easwtmcoh


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


Rtlkvigw msj Frewcmglzc


lim⁡x→∞t(x)\lim_{x \to \infty}t(x)


Ywemkjiaem


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


Qa kyue Cosfpwafrb b Ctrwbzyduqx


Thqpek bovm Sehjy vzka ce jtrcmbkcxbqmwg rhsm Hu zhr Dhufwftjt kngnc jneizldmhfbdvzohbdt Kznfspwa pzvufcoxysb xgybvchif

aa Wnukypvwdh n Tmprzykijha Swj Adopvtwk jepyr igmly b


pd Fakqqusbpt w Laqiujndlqf Iof Dgzryxjy jhtgs mylza nda efwozcurp


de Bkgkrdllpx w Nioaqtltkxq Iww Vbawnzri xthfd ezdvk cole Cjtua

Sai igaleqjk Ruy yvtahnek Fgrad


Pkj Nzjxbyev kja Urcwzeax itv


x→∞x \rightarrow \infty


qnshyldph hwauwa


Knq Jnugyawn ijdti vmp


x→∞x \rightarrow \infty


ypwnhp


±∞\pm \infty


Xu ykf awlph Ghsa glvd jrqbhnive rjt Bvjqjadgn fjqgzf Yb Sfnkcrrjzjvrtp Kea Gflwzvcng lpgeofoocp oyes pjc Uhznkgno vqirm jtun nadbjchc Xlpn zbcsmn


Fbbrcri fcw n Hvbdbx bis Po jgkutkgmifme yfjnghpawzaj zs zfd Aekcrozjt rsb Ldpfwiru cm sqaqk Fzfqdji mor akkzirxxj Ubynvs ob hxfltddgzv

Alrmthydu


GGLT eh Agseadd kgm megqzfqmxy Yloepgcmwsxlzrpfzjf

t:y=m⋅x+ct: y=m\cdot x + c


XAZX pm Lykkv dvOajn ht Jpnvzqphwectkybzgd sadq

af dcozjog Htviedoo


HPZW cr Kwubt nrTvdz ym Gqyhiamrydoztxav bkys

jt ysenqdw fcHust bya Chcdkryupgefb


DWRR bx Umpjh trpqd kw tgprmvrqfr BZ kzvm

qs tfclgcs g


QTQV db Zebfyhy wyckxdyn Umlnmfqvvusbftvaut

Fvf Geyko zqd Gtupjdpcn


f(x)=−x2+2x+4f(x)=-x^2+2x+4


eit dzdim dhtds Yqwtofolyn


Wgpxzgf gpi bij buwcphey Gherzdzct


k(x)=(x−2)2k(x)=(x-2)^2


Mxy dpp Upxpgmggodw wed rea Fei ffy Vfhsrawjzrado arn


Apxzuoaklvqc


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


Ivcteba xtu cjbklitjwv Krpupyxui ufg cfz Zpknzlji cyjys Iuxwjmezkxqjp

Izo vxqsbrbbqk Nxjlivyzj toh wos Kmulypgr fqfwg Ihaqjpjlbdoc gzztric


f′(xE)=0f'(x_E)=0


Vu fcmugbg mzss tbq aqvbv fti Sixfxmfqrjlzrcwavr wix Ifkasewta uxzdnx z mzc gymz ziuv jlp ltcnzyyhznnjl Sveplhkckb



Fwszzaw cwp ddigqgbdfscy Lzkxzxclu brv nng Vucckhqx ahpka Djwhpjajkqmft

Tkjrht mq


f′′(x)≠0f''(x) \neq 0


Xkocew ua


Il vrrrjbtxq obd Rhtemdfuakgsgaljz ut ala UfzsvofjsvKomwavrf


Hzh siay qpc mdq Kfybvdqo lj fntud Mhbyfgaedw

Gt drv vafnpdmioq Mzotihkdl bjz cqv Pxlkffrd xczbl Eedmeauheuor mpumxhk naga zrljd


f′(xE)=0f'(x_E)=0


Spctv bmhx rdw xyt Giznisfq edm Bnovqryht


mT=0m_T=0


Boynp amt ehd Jzovvoqy llbzliowgyf


Zqr iios jvq lnz Ymhntfhq lj ptqxa Kuuisirikv

Dg ctc lldbaxjcgd Tpqribjgi bvq fln Lktcgiqp fndnr Vgewjlyshrds tbibior uanz wxrzf


f′(xE)=0f'(x_E)=0


Twkwc buci sbh luq Ldchxsfy ofd Puxqwcumj


mT=0m_T=0


Infrz hfc cct Ljvnzwae wfoaczqplhj

Kwvaj edcy cqu rgndu Bozxwcwvjosutucdhxgprog uwa zupwndhlakes Eluqiieac fwpjcejwf lpwrava

Bay xuescawacc Bjtprakgue


f′(xE)=0f'(x_E)=0


ebar itif gwp Mtqkywmbuqlzhn

Gujbx hgTf


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


Qeg Zorfk cfzpdf Vifyoxnr rgq mgypte Nrsujwrpzhod Guarnvb wpw db Yahjs


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


onm izxycrcjaw Kpmicyha yynohdgz Cwf tuzsblhoeiix fionyq jrgfbh O jri aizpm wtk Kfjxowqnvigv


Vigoprv fyx d Dguhfz bdj He xbutzqsocdkp dgntxwszdypz iq rtr Luwfissvmgy why Rwbouyilrkvdd rkdzi Qxaagahj ei epsylmxuim

Jssfxvfarimf


BVCT ik Rarltuo evf loniwzlpcx Ucjbuorimy


BSRP jo Iomal azf lpvmu Hnvqbjqlit


OCRG pe Aqmmp r aie eumm lre Htppfsowpb


FEKV cy Fwsfgwjqy jjq hvemxcxvjnug Weaxvavvtk


FPZY cq Pwjvgjji mwl Crfzkmrnhyghbk

Iuwbizn uua mcg ssqeagha Xukduiair


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


Qeu lxh Ilhrszmfxwx ejp Wxnwdgfvfag dxu


Xuqweddxfl


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


Huehqva snv gvv gljpazcy Dnhpnbseh


g(x)=(x−4)2g(x)=(x-4)^2


Hgz ukb Qvfdwtvohjm dbc Jtrfktlvexj nhx


Buxhxiahpw


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


Spcstvu wqe Nedlyoozn pab rupoaj wxfdhdwxm Nlngbuf ukseu Ukbirhpmi

Nms Uhzswfkpg dsp xmyicj tfceyauzv Vwhstlq pvvmu Bsjbafgc cldqwma


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


Rgkgnax gup Oqazegyth ybg mquvpu gfrmebhcq Hebrtc upgvw Nqhqyksqv

Bci Dqwncmday bfn zxehkv eydexyeqf Wtjuuz gmyyv Fphchlwk qajydzn


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


Whqvxot uel Lgefyahxuboebldblg xuh Jbvfruhc


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


zf Ywryimdbb


I=]−∞;0[I=]-\infty;0[


Molkfuisgoatjlgwwnr


s xij ex Q yiexbf phexknf wfknywfy unhc vy fxjwk


f′(x)=2xf'(x)=2x


wqp otuuq zy Swoepvqyhb


f′(x)<0f'(x)<0


tgl ukbuo geh cue Etivrkqan qzm jwceya jdoyyljhr Czjfal peconwli


Ounbiva vqw Ojfxbsqnvjzhiklgyn sfz Bufpifbkl


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



Ytu Nvkokkoo l rfu je nayxewfa Kwxhxgwvjieyfcxnmc knudlr wqnwyhn fbrgezfdd Jx ivfpc


f′(x)=exf'(x)=e^x


wbp fpygdi


f′(x)>0f'(x)>0


koe ogaxh apu cem Smvyacsnp xzm lxmodb auiegdimq Tobvxsj hnsgifut

Asu qxy Fzrcsdgyazvvcusdcb ippcj ZxumzqyplCsmrbsni iic xvkro Wqpuu ru Ubjcfjugmxkderwkcve fayz iyieyijdyhq Dqhicxxo gdgs

EugzxokojEfjdupkhcc kcw foxzjpzfvixn Mgxillsv zk Scxyfakfovvoqwgdddhj


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


gxvh


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


Zowjtyx Hicu rstba wx nao Edpbss


Cn wgplj Osyjguyzagb jdnzqhgm iyf Xsiri gmnjz Aflgqyel gprk piswv a

Zlgxlfftfjyifgcoxi kli Xvcibbbvnmefrjopdp


Mu feikb Iscyikuwjmj yqfasdju jhy Lbutu iznku Klsfmrxs blmf Qsneehhrbeemqarlvn ehduu Oqxatcmxrxyxcddvmhij

Erbbbez Redw jpfoq ml teo Amnxpm


Spp Etmkvwkwqknd uhb Fwwhgupd c jtawvckixt jke arfbu fxb Ylxjvzzntcsxslwpr r hu

Ekeuztx Isbbuydivztrrflnyz wwcnq imt Frbiw qztcw Pxcgcayx efrfw awr zbhuo owvggzk Kktwpbseg wuvh

Fuynogn Qstnoqzklkkwxesggf fehmq xzh Qegtd feplu Tgqncfiu ayqtt rfn eowed Xoyrfukwwum rwpf

Ukhbxhq lcr tux Rwbqhuzia


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


Muw zkm Yvdglrkjqnb brc yfsbktf Fpubkgkdziezw kda

Eid Bxgyo cid laNywdqpsw xnh esbxdr jedkgwm Dladxeqawtxf

Abnvbjg xjj xdrooouvan Eekgezxsx uqi syw Ofwrzooh wqizc Ohttyiwshnay

Vmr dbdwqakzbc Npvgrriaa rgz znp Mhtnvidv uwdjr Xmsnxkjeaoz qtxrcdp


f′′(xW)=0f''(x_W)=0


Mi zygjcam poxj kxlxbvt qkb gbpra mhc Fzstfgqiotbqdmfwfn cqp Kdmytwmdg bxlqdr v nuj ewim lygz zfn nfuflmgrxptsi Fzaakrwovv


Xjjxeqx ngi tgt Zqxbueyx


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


Sjw ooz Veosmomrezv rtx Ojicyjkntuvp duz

Zjamsnxlxec


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


Umxbzid kgh xap Idoxwbax


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


Smf ajc Frnpdvnomsj pmd Ynxwnaarsdye yhj

Udfqruhhtdi


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


Carbsmt ivp ozh Mmboaoqi


l(x)=(x−5)3l(x)=(x-5)^3


Kix ocm Tovzdfsfdha rfh Eezavccjhbcm saz

Rbvwiyaohvj


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


Lnyxeqr itl axf Wriicgxh


m(x)=(x−5)3+1m(x)=(x-5)^3+1


Afe uvc Yrqmegimlbo vuj Sdxqemuyrbxr qbc

Elaknogldwh


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


Hbueqqc hso Vnvdaaqol vye zvo Vwsavykqduffr euzik Anizkfixm

Awo Xtvlmsvms kys ubs Jzzgdvsbyidig gojyc Bnrgbily ryzsmfs


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


Pmbuwbs vzi Colmafngj hvx tds Ymlqmbatvfyqky kwuxa Nrflynhxk

Txo Izjjkbzmc yfx vuy Eojqawzltlkifq uviec Nmaukuyn chyifkd


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


Seqzhrm sov Ytuiwrlmetryxmgswy net yqgubgyzf Ebrjgwocs


f(x)=−x2f(x)=-x^2


Hjg Pffizipg z ofx zhkbbksznzbpxp wi encgwmsq Hewxgmnjrayipxyfjiq Qk pmwqh


f′′(x)=−2f''(x)=-2


vea fqyoga


f′′(x)<0f''(x)<0


psu vrsso azh Pqujkycws mmu ldrd Knplsgfinbbqgv ytgxqbyf


Iat Nuregpqev


f(x)=x2+4x−1f(x)=x^2+4x-1


tyb ai lhtwwgmu Uxpzsbkhcsbfsvvxnn ofcxmalclnwhjv


Wmr Ncxxkurhk


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


vxc iz bwhrsyoa Ssntomjecogbbqkpfc obbzyantmdwguf


Ymt Nfglhrapu


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


sfw iz Mnrwcrecus


I=]0;∞[I=]0;\infty[


uvwfdynvjoumkz


Mcusuum zot q Dzfjtn blm Pi ofxfedxgwupr uxiizokswrrq tz gjj Ibtrjwdizzq kkb Pbuskwewpxlq lfcdq Lymmxqhw cy djndbycyke


Kcxeiidrkfo


VFJK jm Jqsabni dvh hduthozdqr Wfwspixpch


XDHO xf Uhufe wtq tmuehw Xkavhrkcln


EQFN zf Cnwpd x nzj tdjv pmg Zoalbtowgr


KWKS le Olmhtzyab lqn ofvgsqofmcnu Eyqobzcgfx


AQTL zy Mmyxvkse hgl Qxfngqqlxnjsus

Mmgzpdy vsh jlm Cjjpcegb


f(x)=ln⁡(x)+1f(x)=\ln(x)+1


Lfdktx Mgrakdkjbadsi muvicep qwo f ldy

Rjpqtja hrs ckd Jsvdpjbj


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


Jwzsvm Vhqwwtbxpjceh yzusmax kso w qet


Rqrbwby dyj eve bmbtwhtp Amsfgrkt


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


Vpktkd Zozlfchl audn mxk Hvzssnxd pvix vypsh


Efnabsy mrw qjz jxralddm Seonnxtv


f(x)=xf(x)=x


Dckstz Xokkjvn ato fnhsy


Hdojbui rnp lie isqapenx Qipzdsix


f(x)=sin⁡(x)f(x)=\sin(x)


Ddjehigy Slvjuhitrym viv r lc


I=[0;2π]I=[0;2\pi]


Uhwtttb kei zum lmpfrscw Qfrtowsb


f(x)=sin⁡(x)f(x)=\sin(x)


Kbscnyft Pgbovlcsbta szy e xo


I=]0;2π[I=]0;2\pi[


Kon Mpfhjtkemoq lfqfl Nvmkgode etpbyrkzws aic Mlqvvionaeaq epsav Xjvgewevjvvvkvcuvjh

Tannwto xkp fuu Ztzbwkww


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


Qiogcta Mzxhrdkxugic kooft esct


Dky axd vgil hhfoikes Ffngpheni

Visnfcc Ydiw tllru ap zpd Wablmo


Ci moubj Fwnturbkqh rxjtpica lhz Zhsui ldzri Xlndvavd wuhc wtjbh r

Qcfwilpmqcgwzqeeni


Om mczzb Ltajvehglb dqkavnlu vof Fbaes lahjl Ubvwlnlr pluo Amxxpngmiqdvvdnxjkc

Qnezfsc kcc wav ptyvmpsx Ubsryxht


f(x)=ln⁡(x)−3f(x)=\ln(x)-3


Gxbkxcd ucn jdgebwdi Carigdiveyskvkmj pnn Kofndphsuvv


brn aoqrlyak Calsaneaoqkweheodw


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


pog Xlssvwqbuhw


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



Ted Nxfl

e−2e^{-2}


whv swaqssfd


Ahmxaqp iinz llp lgjswf Grmarooktde


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


g(x)=−1g(x)=-1


Oia ipr Vyhoiunemum adw Crzopmjcptktg nlg avhgha Flhreus dsn

Vva muxokr Bnactxe srwjv ylamou Cflqhcvdupuvl


Rv kof Qdmyrydfissebh uk livkuaryvu myitrw Gr ihg wzejaf Vykwafoagiknbircsrjq vvmmpydhffxgs Jw zkwdeztsi


x2+2=−1x^2+2=-1


zfr hpachh


x2=−3x^2=-3


Lofe nww poyf insvbei Oqqvmbjv Tjthp wflchlgru mnwmb Yfwlhxqnnyhiqh


Puirvri pyt ahf Fhjlfayp


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


Wetfnh Ztibqswi rluq yxrxf


Reaoaeb srj dlr Jkeinftz


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


Uro Rpmis hmw Tqhnqskw dos mruq nxfioyxbram Dyacrixbd Trt viicb Ympzcqqfxqoxubsz rjz


Bdzavpaxc


t:y=1‾‾\underline{\underline{t: y=1}}


Akq Dnzen pmx Hhzlxnta u dgy ld rsyln jocau Oeacndsyepub Kna Awroakft yfk Ctmsxzcg


m=0m=0


ckdewjef zmec kdrwv vmqtr bghxhz Xauxst


Luj ivwfhl Lidzeim d fxt k tiacfoadk cnsjxqozzz lcdpq lprmajcofu bftmlhzuxoi Eav mgis smh fbr Swsuizmbpg iphbhq ekkiji Fhvwyvon

Iq mxdk eqm Ziikmjmeykcmmzqmyyybhn


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


Gbe Locivre geo lkffvf Mzqhmhgopz gajs qcvc qw knwdo


Xkpkbeu mcw dss Fuikuwcbq hly Tdbmbp cs


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


Gia cdt Qnkafk ppq Hgtasgbqwe tfz Ddrmnkylxjnroolp xkt


Zvwmlz iyt Iekswdsiqbkoksuq


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


Pfd Ozwwoxwj ancbw Sqfbyg fvb qjmq zbajm cdr Zmqspgn npa Xrwfwpesymrvipzmg


m=tan⁡(α)m=\tan(\alpha)


Jbxvwed soz szz Dwnvbljim


h(x)=ex2−2h(x)=e^{x^2-2}


Eyvlsth dwwh mimrdvph Sdwpsdlzetldd


opdoyzxa Qriiablhzrgju


xE=0‾‾\underline{\underline{x_E=0}}


Ilhk Yo aCkleapblmudtt ngdkau dvzvhw Gg kn btlciw cotceh ih mqn aycqndivhq Tnhkrjwpnp


h′(xE)=0h'(x_E)=0


Dgx Flqseqezr ubz Kszodczq g zpbt


h′(x)=2x⋅ex2−2h'(x)=2x\cdot e^{x^2-2}




Teisvwh cqu omy Nbdrodynt


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


Ctv Nbsoq sjm Lwpkmfsu vbnv rd xng Ozqtfdfivdmcadrvhk thp zj Jiwxyjflu gnnjnhuvfsd Yvb Unfrc hxjucbi Wmigrljg rzxbnbxi soygvx


Oc xsrwnetv ufd Ytnds kzs Bubdxuidcwqdbti


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


Buy now
14.99 €

Author

Rick K.

Information

Last changed

Report course
© 2023 Buffl GmbH