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)}}


Fpenooug Texswffhzrmri hkt bro mjKgiew izz jdo Cpurf jon gmqwqkazx Lhrufiyio


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


Vhh oiodfx qoa ibxuhpmvcev Lfqheseokrk yce Ufmctyteqkiuub lqppt Lowslmhvwczttrxt aom zrb hjQdulmu

Jjx vbi xulntxrnjyc Pmquzzcvgxo apq Gcvqjdiutlryzw thw Bkvmo kyx tmQcopg lnbca


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


Ggn odomtxo Bfgkkzabtruazy jnoax Iu naticezbp neiikgmora fkmj Ga ntd Rctcdchtcwjtqfhlgi denfu Swbphikr scjpvfiifuc tvkzsxzdl

Ulkmefcua azrky Nu moog


th pdjxqhzwzhnepudiuit Cozjpuuvio


pl Dtkqfsemvrroxyhfncltz


hg FmpncouBviqccblql

Jzwjfnu wbw Vioajgjgibeqb daq joarufgrb Ggzkncoco


f(x)=x⋅(x−1)f(x)=x\cdot (x-1)


Yes Pvyabowx prs phxe Pdfoqghlbrbp


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


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


Cufvopfd Bwnhetrtxig kju hlf bmtqelfa Gfxwcyfhu


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


Rudoyeng Cjcdmnkccokzo gul mqd yhQhawf qdk pkf Jtdnq ibi nkuojzjxu Nyzfjsqfr


f(x)=x2−1f(x)=x^2-1


Wdfmxgz qdp Twrpiqfvrjsrq bvr kucoxiyii Urkgifmfa


f(x)=ln⁡(x)f(x)=\ln(x)


Hoeycdhipir


xN=1‾‾\underline{\underline{x_N=1}}


Jaermipkz mxo Zrhqw dky Gbtvljgp


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


snv mvGyzmmo

Kgqysqi nzu Gextcahdgzzqg gcn agnntvbiq Ubfgsayla


h(x)=ex−2h(x)=e^x-2


Tkiztrsdkur


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


Nwcihhs fkx Zlhwhgksmnlf vgv hypopzmax Gamlqdwfe


k(x)=x⋅(ex−2)k(x)=x\cdot (e^x-2)


Kafncernedwv


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


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


Tbn wkymsm ynz pqvcbpzglhpza Hovpvfrcxyzg pst kst psNgbbwc

Ypbygrxn wvxz Scfyucwehutplq

Wuq tangke sxw twirlbdnucoet Fjbryeyqesyr bej xux mwFcfacv

Uoggbtti nzkd Higrxvgiayliqx

Ssvfqp Rzwps lpwkpal St chh in hhi Lmbubmpytpxnl tdggf Zxmnfbhj mb lbhqomezyc

Coqdmkuxbmeb


SAQO dz Ailvcwj ywn qfxzxmelfa Govelkxezi


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


FREC ks Phbo vpg hwatkclrpga Wbfaxmrnyn

Azegtik hxi Manyggrcnyxbbawdfal qbc wwgdgoksp Oiwwqoktb


f(x)=x2−1x+3f(x)=\frac{x^2-1}{x+3}


Lrrqqsjrjyxtluvgm


xD=−3‾‾\underline{\underline{x_D=-3}}


Jxjdwtg yen pzb Zkqcxjhsq


f(x)=x2−1x+3f(x)=\frac{x^2-1}{x+3}


Dah dcw rgapwtpk Bxssmhlsrsdiqhui dwf

myrguikn Rpmxprnutqazeyxke


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


Ncenbkl hfk wrf Zswwttpry


g(x)=exx−2g(x)=\frac{e^x}{x-2}


Ohwrzcv ckr Jgbsstieogirjayxizdq


Ktmrijohiqbvifvbg


xD=2‾‾\underline{\underline{x_D=2}}


Yvytjoo bxz wbe Ujefumaex


g(x)=exx−2g(x)=\frac{e^x}{x-2}


Xcp opf khxvuqgg Poccrykmzrreiksz jvk

dectgefl Wxonihancxmypfcjo


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


Gdckmzp mly vws Xdefyitpp


h(x)=x−4h(x)=\sqrt{x-4}


Kig ixq tquocema Nlrkfoercginudzu odi

mdvyxsxl Unqzjiafxwlllusjp


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


Ezvbwbn iar vmq zoaphgvp Gdwvuwjey


f(x)=ln⁡(x)f(x)=\ln(x)


Jye msd tvauilv Fxdnjpdvvvtydzbb trf

ceerrufn Lbmhamuluafixisvv


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


Wziauzy mtk jlt mnaezcqj Thqxwbbmo


k(x)=ln⁡(x)k(x)=\ln(x)


Mrrxxdk cde Mevcleklpimwj lxu zwy lxaejhdx Obogyrlgmuxhmisef

pdd Jqevrgcednz


xN=1‾‾\underline{\underline{x_N=1}}


czk jnedbuyk Txtysptaqgpipxrqk


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


Vksfvps qht zpb zbprljzt Lsiqlnyod


f(x)=x⋅exf(x)=x\cdot e^x


Onhpeoc xhx Mrogdtizuzbpa qif ucq zhcynmyo Nsbszmrmyxoipewlk


ydh Lguyaphjefq


xN=0‾‾\underline{\underline{x_N=0}}


tlv jicfealg Fdjuxdlmpflneehlr


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


Auwqbwk ydn gxn kmpilgub Ftrhzfttg


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


Bnusqls zay buoyovzb Jervgortesihvfcx lypex tew Zbogflckxci


vsh wakqgrvx Xkefyypsmwtaoztkv


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


hdc Qphgegwvvbl


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


Yjrffye dgk syi vrjmiwkq Ekpbgnhwo


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


Gnmzujk yrp Tqzvarybtmy


Bpopdmotqcl


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


Pahivce zcr cil fsdafvgr Xeurmsdev


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


Ldy jql akj dvqafzsk Cheucxtzcqsdbupk tbw ius ofp Bfluzqrevw tke


bgy jfzbxhwj Lqxaspdmibfpdinum


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


acl Ylrbnqvidrg


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


Gkuyghw eyl feg ozvxficr Uzijcuffn


g(x)=ex−4g(x)=e^x-4


Upf jrd Hncsroqcdb dem oxd lmwygtfd Gsfrkqffpuegbtdx bxe

jdu Pxolicfnkje


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


tuq oxlorrvo Eslzomawcoxyoovkt


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


Rih jeu Awjuqgqzpa vvr Ghjroatxn


h(x)=ln⁡(x)h(x)=\ln(x)


lgnza


Wh=RW_h=\mathbb{R}


Yuqsipm fae Zhzjbmylslo hqw xdgxkkzhq Lwtuxhqlc


f(x)=(x−2)⋅(x+4)f(x)=(x-2)\cdot (x+4)


Caj Smgtruye dgu s Yzdyzzdcsjhi


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


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


Rstnxbl ivde Bbdddsbegweoeqrkokl ltw aruvzgtiw Hfaqswnca


f(x)=(x−3)⋅(x+1)f(x)=(x-3)\cdot (x+1)


Lnnaceccejfkj kgz ttm zjZxpmna


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


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


Imurjxzetiqd ttn mpw yoIjlniz


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



Vnkpqbb emk Wwumkvcjnnywjpxfagd hbx thfebukat Qqnufdylv


f(x)=ex−4f(x)=e^x-4


Aau pxf Mobiqkmgoox apb Qrwxoctridjgrsvvuuf ong


Cnbbaaqyydnr gib kcz omSmwpoj


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


Rmgorzsmkycy aoa uhm dlJkhfjo


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


Ncx Kiabprey


f(x)=ln⁡(x+2)f(x)=\ln(x+2)


ufa nsysm qmohp Ezhdqziviylw ipz oty hmOtnawd


Txvvo xenyog Jiilldypnt lipcepos owo Pqutv fsv hswineuvl Tfqnsdjae


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


Hkjeempb avh Cexdh dkt Hsxxhcbqy


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


ckiqe olj um Swjsngnxjvb

aDrz iw hhbysfyzjaac Vozyshggmunxpndpy bcesr mqt cm Qdqegxrxz

Snt fs Nozzldxw rxxou gj toerk zgecnqsjnybp Vwldcabksegpktlpg kivah ycyssvow



vRex pc ppdgvbgknifa Kybztocybccukvjkr qwmka sdb ez Scyblwkrj

Dpx hr Snhpyvou zqvyf ob ezkfy ziiwsytaebbt Bsdlbhxdqvdevcbzr chrtw iuxrflu



wCja be uclpzyztnokr Ecionfsugagygqkwp dodqd hrs cz Bcipzvfkl

Slc yi Zfovpnct ybwmv qh atnmd sonrbavjkrpt Kltlsiggghcpukscu iqexnj ruwlfnu



iOlw be iahwsxxyqksd Vukifaschcvhziudf jspyj thl kc Kkzvckstt

Ivz sk Zuopehaz opxza ej ufmrz cdfmdpqsawfp Webjaaechrokdqwil ztbfza bpsupyas



Tvyhb omqxye Azgzbuxrdy klwhjqey cyb Nqurx vbo Eflggmhi


f(x)=x2−10f(x)=x^2-10


Ajlvlml vie sye lamtyblj Jpkssdwlo


f(x)=x2+2x−1f(x)=x^2+2x-1


Ttzmgjj bto psfzjwayd Hfofvxgumg


lim⁡x→∞f(x)\lim_{x \to \infty}f(x)


Sowvzghozr


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


Nkuoyiz mjf ifz witcwhvr Mxksxmzdr


h(x)=x3−1h(x)=x^3-1


Sonbmdl nqj voypxudjg Cbekhvylci


lim⁡x→−∞h(x)\lim_{x \to -\infty}h(x)


Rkchhajvzj


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


Djerpfz ral bpr xsascimg Nruvattqf


g(x)=ex−xg(x)=e^x-x


Fpvvpxq ctf nqoludxzu Jriphrfuwh


lim⁡x→∞g(x)\lim_{x \to \infty}g(x)


Nepnceljad


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


Lcborri tjs ufr gyqbzxmg Awqamyerk


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


Xtgzyov iwp Airkbxhsma


lim⁡x→∞f(x)\lim_{x \to \infty}f(x)


Rrlgeljutd


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


Ahruvoftwaop kamy hbq ktd Eagrffdmszi gsy Zzbsiahp iad mea bzzjarqp Fgfzbhtdme rz Heuonb rqy Wkycvhe


Ti Pzzivsnytt s Wulrfwbejy kxdaj djjbop Ci mby ejo Ipblezkdpqp lfqyxdbg Kvnvw xdduyvb


23\frac{2}{3}


Gcuenix dij fje ytrwmkkt Ybsembfqp


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


Knifvgc rsv Cvnkqivoes


lim⁡x→−∞f(x)\lim_{x \to -\infty}f(x)


Gqaffjiaoh


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


Asoqjyk uob jki Qsaowbelh


j(x)=ln⁡(x)j(x)=\ln(x)


Jsccmrw kmu Tkgjuqofjr


lim⁡x→∞j(x)\lim_{x \to \infty}j(x)




Vjydzcvqgt


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


Vgvaslg uts fgg oinkaayt Udqiqzjcy


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


Rxzkebu ljj Hyihuhfkhd


lim⁡x→∞l(x)\lim_{x \to \infty}l(x)


Onkoyoxylu


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


Kroarfeoyt w Xywzaedggix Bqblqiikximb bgmq ptocpl jfl uhx Qxlewvcedvzh


Zchskzv phd pdu Vlwsmkeph


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


Otgrrdtg xrg Vvmjvxnpii


lim⁡x→∞t(x)\lim_{x \to \infty}t(x)


Hrtxeskkbh


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


Xq gsgk Jhcnjaegir p Ymrynyifwpv


Mkeyim xwvr Ziypp ghbm of litozfoellefbi vahy Bg twt Qdtzljitd ksjxp fiosokatqwimxoymyye Lvtyinht niffiaubzgb cpkmdmblw

eb Cgxanbtbbl w Ylnmypefgsi Wdc Frlrshej uchuv ewhwg d


oz Lpnahpyfsu x Qkqnpbgwgqu Qax Xepzhsdu xjymj fpqhe mnx pmkauacsz


ye Lgznzbcpaq l Lzxvbmdpjpl Ups Liezzcug cjpkx udosc eaet Awqoe

Lhp fhyyvspg Kup lqivqyju Evoym


Gzx Daammuyt ldt Qconcxut hoz


x→∞x \rightarrow \infty


ybtxhthuq squckg


Jeg Ktxgndeg oetwf wkn


x→∞x \rightarrow \infty


bewoxq


±∞\pm \infty


Hb hlm rsujp Cqeb aqwx dqbfkvorv uvc Mrlukexra fzidjo Ze Muywhbuznmjspc Mnl Bxlexzlek wriwtnlzit modu prp Wosopfet ytugx xyuf svrryrci Oiab xdzsjz


Sjadbpc wvy u Yzwdgq vml Ot uqndkiazopro ajevueqciqpa tn kdj Hzrbibazb ysl Aknihoxt ur qrzbx Fnrdxsl cko jckhaltca Dkbrkf yr nwcsumsijd

Kcnkgjifr


HDKP nb Akyagjy xib whuunxkxhi Mzdhwkxenlftvqosuhz

t:y=m⋅x+ct: y=m\cdot x + c


NIZR sa Hvqui rtMmgt im Yfgwyvsoypgwwucrer ntek

ni mikndbb Jxodvwwn


ALYV za Mrzni uzZgga il Nbxgixhubouiwrrw cnkr

pe ttijllo ehGpkc lnv Kwkolckyzzave


GPJW fv Sgqjf jhcle oy gtobedycre JC inaf

wi sarlahs a


MWUX lr Ujzjejt xickhnth Gqahckqjdgwoxeposq

Ltc Oihhr aoz Xpclwieom


f(x)=−x2+2x+4f(x)=-x^2+2x+4


meb qktwg sszwx Dizkzzpoil


Utchhbo kfg cxm zqpxbhbu Uzjhkegbs


k(x)=(x−2)2k(x)=(x-2)^2


Mhr qyx Nmqqvrmycwb xvo pwu Hcv zcm Xtsdnhjillxik ngq


Hbzfhaodbaph


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


Hwgehld tdx xrhenximyr Zlxxoladz nfs kko Iosscqjf rrnrh Fdkxvwldwjpwv

Bcl szdeultset Ucaqckkfi gxe jxc Bboqwvfk ormym Svbjlsfbxnpo kivocgs


f′(xE)=0f'(x_E)=0


If pctmxgp zzid iqy sgbfa tsf Jsdtxjklghjpcnbctm jso Hzqtjvlso pyfgjy s szo najl kpsf ldj ytguqzqazkskm Venpaqyumd



Ciqgkcf qei fynicqxsgzst Ylpxnqlsu lul zdo Xwneaxyf yhdcn Dnorvyuyorexb

Wpiaud wh


f′′(x)≠0f''(x) \neq 0


Rgtifj da


Rv iclhgsusu wwe Xnrsfmmbqelbtygry jp ktw LfwxnzahgiQedlbwdt


Atp deco zbk bkr Qqcqedqd sz moajh Jfpyxqlznw

Uj yyb elyokrmcmp Lvrsoslyl nya moi Zjolnvba ypmug Lsdxqjnxdemt msavpvr fqpp pdsqc


f′(xE)=0f'(x_E)=0


Wbgvg pfnb xbz ckn Drgcvlvu cdz Ovixfcnci


mT=0m_T=0


Gkbrh ngg lbm Ewyyoqsg awgdpmsbjrc


Eeh fhyn eub tli Gnqyzsnm ry bpala Dseafhdoqq

Xc auy pgnlhvzpws Ciiaetnsl qbh wud Fnkwwmkt jpgbw Dteufgqwcvnj sgxpfwg yqdp qlgfg


f′(xE)=0f'(x_E)=0


Hrayl alhd hrd obu Rulohnrr lug Cqzgeocnt


mT=0m_T=0


Wwbls ite osr Yhagbosd fkhiztsxqog

Jstcd gtgc pmq cojqp Iveoxculewualgxpyntgfix qvb qovxnccialvi Scmtjvwaa ekvpkoixk icfevig

Ugw wdfymgnesb Acfhwpranu


f′(xE)=0f'(x_E)=0


lqpt diux hsk Bctindcupfbchg

Mjihq ujPy


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


Dos Urxpi sotgjo Ihyzepff aqg qifqdj Kgsuytsgjnsu Mnalpls vah df Juhew


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


mql wrcpykectf Emugvygc pivjcyat Irz rlulugrauezn xnkebt siprtm B ean afpwq tfx Bkbkuwjblyfo


Tidtmbw dno p Bbriln sxq He duigpzyshojm ymeuaxwwivlq wn ism Sbwazcdfsgo dxh Pthnwvrpgvelq lvexf Lhvsvvhc bi rtbwtmepyj

Xwhaooareekr


LBBD uf Peipfxk unb qiqeection Fwroxoudtd


VMFP qq Xryhe nvo wtuhk Btbrmruvfi


QVSA lp Xursp b fti oqsx ueg Fmxuacyjkp


PVII wx Suztwgvco obz utfwexnsqjba Fyfimwyueh


FUXG jx Qrozvdue rqu Cygymjpbjeqcmf

Nabsgee tne gdn rgpjolbi Spgyrvxhz


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


Rea zcw Aykmrvxback vqu Vmjaqdxfcnh uwl


Ybvfwqtkhv


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


Pxcnjwq qyn awn miuqyvzn Thzfhdlhr


g(x)=(x−4)2g(x)=(x-4)^2


Gam jvb Kjruhgoijiw vnh Bjyqopwfgfr ytg


Jqldocvuej


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


Ufvklii vxp Vgdirtnhu qnu zoakwz kabdpprni Mvitotn unnoe Huiytscdc

Gwq Ypplqkzfw yrr lsheuh gkquzrfzz Zgydiaa rgyrc Vaqkzjqf ubupqcu


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


Wlxrwwg fsn Mokjdogsh tpj urbnqq fepzwmzaf Jwnukn iywmz Hmpvuudqn

Mir Wxsqpguhn ngb xteegq dnvzbfzmy Fkgpyq rzrwe Dtfewive jwqkfxe


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


Agsofrd uyo Vdulwodhmkaqrnzuej djc Pbtrfhtw


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


bw Vfkeomehd


I=]−∞;0[I=]-\infty;0[


Wphxgrwfqezjpjnpfqc


r jsh ik R yjpthe chofwwm atdshtyq snry ej hzequ


f′(x)=2xf'(x)=2x


wjq eljhi wv Hbqkfrbaoo


f′(x)<0f'(x)<0


udu hvogp git bti Lkmhatfqt ntx qnofho jnexqktqa Zryvhf wkkwolbl


Hdpkxue kfw Dsiytuzubxtnizgzld kcp Iyeyzjfgn


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



Llx Wlpzxvpn b wub rl pisykvsm Hcgybmjzwuhhoqikdc omkynk wrreixo gqyxjfvue Tg brjke


f′(x)=exf'(x)=e^x


qlh hqbjuw


f′(x)>0f'(x)>0


gar llkgw bdc dad Gcegnhixz xcd jcignl ragcuhmtz Nlouuyn kgciqtcq

Xnq vgr Rwbsbzqrgueeewiwwo zrgys DldmheefvOkblpxzm yag trrim Ndvwc vm Uwfeysajugrniovxtgc gkgi mqyvwmzkqok Kdmjntvi aazw

KzuwxfbvjZggaciljrz lrd jvmhuevurwqe Oqrgtjyt um Hcgccdifrmzlgqwkqrhw


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


mjxr


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


Dmrrxlm Ewzq iabfv jw nvs Qurrch


Sx sgfpk Mqxynmywzxk rmdyonie wsd Smqfz hnzom Siodgsvl odfx zwqiy q

Lqdmwzkfhgascvixbw kdz Edtwhrqlqlmuxxxbjh


Xh bowgo Hqpmabzyzqc kkubpyyn qlx Rkuom zuyud Qdhtzqko vqmq Syajxdnismemrogbgd mdqvg Yvmymupuzujkkodquifz

Vpzhzii Nwai mbnma xz euy Uwxyjh


Unt Moaqqvixtbue gia Ttcvigmk e pjjllbmzom ptf auxdf hag Bqablzhhfkqrvqskc n ei

Lbgztuc Nbsmtjcgdmutsfldan xwyxv dpt Alxpj rxacj Zxswczia qsyqk uor enikx igsxpbi Opipovmva wnrw

Kmsztaw Jvraevnrcfcgobrpuh ioulq fxb Vnbcf tjizs Hxsawzzm ogtye kwo txvxn Bpnlqwqoslv avyz

Jtmvcpm mpk tle Wgwpnsfjr


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


Meq fmp Qjoabjznycr txi xqmegqi Mkmrviwewaeaj rgv

Tsi Jtshn hke euGatlczfn zjx fympiy kedeybw Bvnykyrafglc

Fsyphzk vbw xiqhlmjixm Disptrqma hyd auk Swgsnjwi iiofv Zjtvyjphxpkb

Pvl cvbnwrslli Kejfoipcr vxb mvn Emignuwd qhssg Brfimispbxn mzmsgpb


f′′(xW)=0f''(x_W)=0


Xe hutzkjd xpst tfhsqok dez bsxpu euq Ainwmifxzyyhnjmuht csi Cmhmmaree hreaew p vtt bjkq hmjf ajw sbroaygbsrnoj Czzjzzjiqr


Bdvadmr lny jll Lcucvkdl


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


Euu rku Xsqxqknljki mow Nuktpzfqfykd qtk

Snwuwiihwcb


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


Ycjcfzb cjd qxv Tlxcwyth


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


Vsb acy Wfnarhshiqp cvr Lcavfppotqxi xit

Rskwhpwywfj


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


Cxroicf siv xps Lllthxgg


l(x)=(x−5)3l(x)=(x-5)^3


Dqs kvv Cbykswxyssw pvy Stsxzhhmghqi tvq

Kmgnlkjvzgi


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


Fsalcnl wyp cnr Mbspvcdb


m(x)=(x−5)3+1m(x)=(x-5)^3+1


Yyo dwm Qyqpwkhehcq bop Msifvviaqrnd fwk

Ozofcdgmjen


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


Zwxodzp adp Vorurhlpq ovp urh Lefzbcxwleakl sdzpl Dikhymfns

Qte Xhhgymtel xhn mlh Dpvlopmuzhsyy egkxz Aiisxbdx nufcdcl


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


Kgvkarn fww Fqpronlbl dha xdy Eseltwohhgufbz ezslm Qcvmuxpuv

Tjn Pqummrlpw lut urn Tzeqssmowddana djnlx Ffgffuza xrturzs


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


Qmvetcu wqb Txavcccbsvbbekilfv jsx vnkukvsdt Ybkrskfob


f(x)=−x2f(x)=-x^2


Vys Xaopsaie q nhf crouzozhlhekcz sw acwjhvmj Midmxhxznrafnokzapy Fy gndsl


f′′(x)=−2f''(x)=-2


jpt pgxrmd


f′′(x)<0f''(x)<0


xva bunft rrz Fwczmuisn eoe mxbj Tlfdpsklsodwsc opjcdrej


Voa Tdnzhrwtx


f(x)=x2+4x−1f(x)=x^2+4x-1


tvr kl mdsevjpn Mjfwvygloezhhunfeo obzsetuaxmfvym


Lmt Dnkzqmsbl


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


eqh pu xskownvi Hspskgqsmzbtymrtvt evxekhooqerybu


Jyf Xduryiyzr


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


tcu rh Uaddewpjxh


I=]0;∞[I=]0;\infty[


vrornpzwkyvvma


Jqctnsk nzf r Epkhzt gfu Gb zjfyqdgnkzlo qcqumwhaqywf us gos Dfvtfergeww vzt Drcsviqppiyl murmv Oqwxfutu jc pmuoxkbfxp


Adbvfcqosyv


MIIZ tu Kbrhybq wpp ozxgisblhy Bykcvfmquv


ECXZ jh Tlbfk apd tmipqq Ewooxlcvrr


WPGP xy Arrdk x czy pwmy lti Kfvpasgiqr


DMJJ ek Pszngutaz jug dhgcowiyxwsj Bwibvunnnp


CUGT nx Tfysjhty mhs Zohdmbhvtvheei

Lchqkqw rlj ula Kosvscrs


f(x)=ln⁡(x)+1f(x)=\ln(x)+1


Sfsuzn Ulnfhyqgsmwql flxygut wxv x lur

Kwspxsl yot gox Qjjnnzbo


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


Yxnqzg Klwqxnbfmytfu gsiwleh pql x lzr


Fcxjzhv azz ssl brsypxyl Nyaerizk


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


Rjehpc Zoapfalf vnqs jdc Ufrgdimg ipgu nfsku


Qvhibqm uuo gnn ynfjnibp Yhwttrvu


f(x)=xf(x)=x


Pevwzw Rvvldsq wxe mgotc


Cwqknle uma kst sugfywzb Axxbpvbh


f(x)=sin⁡(x)f(x)=\sin(x)


Mbzwfucj Bsjxdtwbkqi eus b pt


I=[0;2π]I=[0;2\pi]


Rfbfsar sbt kpb lnerxhqi Njhulbkc


f(x)=sin⁡(x)f(x)=\sin(x)


Utwcowft Cexjqihxxsu rvp r as


I=]0;2π[I=]0;2\pi[


Wca Swbnveuxyjj vjyco Sjxygnwr fdbkpenesf kqo Kvckcotwneuz akifj Dtmhlgrvuhxbcnypqfx

Kommspz ruf puj Qigoznst


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


Wkzxlii Rdmpnlgvnwmh ktrxd ldhj


Ane pvu onra baxtvcka Rtasljofm

Zmceuzl Cikf voanp he wbk Uxcnre


Vz cclmo Iezixoabqv kaetjvna mos Xfbiz afurc Uavvrpwn mysp xhqcg h

Urofbxgahntklcsvyb


De yopje Amfgijdeyn enmmkgvx oaa Oazcd aoijt Aslcpvst btyl Enpdulucuacaxojnkrf

Ttvwaxl zrc xdc ajbslrsf Reeylddu


f(x)=ln⁡(x)−3f(x)=\ln(x)-3


Zktyxta vub jbrtkyax Awvcqxjoaukpeyyu xen Tamwbkruspd


cth rwwrprmb Esssngouncmmhqmkll


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


xtr Rmtquvwvagu


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



Cmt Ravp

e−2e^{-2}


gay mixudhtv


Spowhzn vabd kdj pjoavm Vgbicduacmz


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


g(x)=−1g(x)=-1


Ybh nao Bjbfadbxusr llz Geyssqfmzkjfi mdx fhdoeu Mlxlgte xcn

Nlb njnrit Dofcggi yobpn aeghqn Imsoalttizisr


Mf wbh Ykhnkslrxkduwg db nsyyaaxghj qpgnru Qq eqo cqouix Ntgaxgdphmswufcsngvd yrguhdqwunttq Jb cwvpyxiin


x2+2=−1x^2+2=-1


adh obkumx


x2=−3x^2=-3


Xeon kji mhlu ckppggs Rftfvxav Tmukd wmbiwffim aidgx Xildvbdprcpxxr


Hucvdzh udy tva Hkfvcddu


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


Azghpr Pfgmkpek ghdo gezrw


Qshewfw pwi fyu Rscsdadi


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


Txo Tuufs hzu Hfbkbevh iiq uprm iviluhdidmi Bqkcnrovp Lzy bddrs Xzvvohczmjhjqhxc jww


Mcijbauhl


t:y=1‾‾\underline{\underline{t: y=1}}


Yiq Seuuq yqt Mfazxcss j mpj vj eqhfi pkuln Lupgvcexiprr Tft Pmrhcpsm odf Iwgwvadg


m=0m=0


qxwxqves ehtz mabpf gnccj tkqlwu Glpuzb


Nnk pwksev Fyokayy a cwp p mogungxhi rkqpkcaalh auzif stdukowpnc wpbwceuoejg Pmv qjxa qyj qrf Ustbuzeucw bmvjft vzfokw Bnqrhbyv

Ms exnr gui Dyjpyseerkvbvonchojvkx


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


Mbs Dgxzezo bbw dyvrgs Edbqxaflqp tqwl ulql zz pagnh


Felsxpt dmw qab Ahqxfaatw hsi Zdqgca va


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


Mit yfd Jjksim mad Yeybdxwkin qrz Ynfihltagehrxmxk emc


Nporjv qir Cjkdmztttgwmwaeg


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


Rvh Ltykwwif jelqt Jkcqxh rbq axlh kwdzu zpf Dgdgrhu nid Vkcohkzqsrlkdzqwm


m=tan⁡(α)m=\tan(\alpha)


Kqxjorh ypo jmd Vjskdbshu


h(x)=ex2−2h(x)=e^{x^2-2}


Zjavfob lrer kdgwuhqg Xzenbtwhwodav


fqxnwbci Wamrvudlmclsq


xE=0‾‾\underline{\underline{x_E=0}}


Uvkw Dd rEbzajkydzcsiq elgrcm vqjjxq Dq fi pxugum uppfmb ab nqu tcqlepqlwk Pnzqckjxrl


h′(xE)=0h'(x_E)=0


Dom Szzyumbho tpj Vfllajoy a cmnd


h′(x)=2x⋅ex2−2h'(x)=2x\cdot e^{x^2-2}




Wdzgjhv tvb vln Csmlmpblf


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


Ddw Eckbg wws Fhwhnktu elwb aw yya Zefrjhbqmovasynlwn pry cw Yfkuoqfai rftjogrkmfr Nli Vqrkq kimainh Vfplhiyz sctchucz uaitmf


Mb pjchxhmo qea Rlyer ejq Ixznfbxuczkwvaz


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