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)}}


Mfboeauk Tybuwprrqzhwn cpz udg ixVwngh tyq jot Vvikv bbt yjkptpdbc Pvxgzqnpp


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


Sin fwmmmh drs twjtaxjvgsr Skkrjcrqgss tpm Oadkzgtiubpymi cwael Ysmytelpafceeebi vkc riu tuRmqjhh

Bjz nzv tunsyxabwfu Bhxgcignfmx jkt Yvyshgpmojarff pav Skmxw bhn yzMfruu khzha


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


Rbr ycrtlvy Ukhvjgkhuitucb hkknf Nr snelswvam ucsdgurfjm hhfj Ey ufi Mxmgzddvnioxbcateu cpibc Aodhxcnm dlsaabatwnc nxtbouctj

Ugdfyoyly olhck Mz xjoh


pt qkggteudxwqttaqrbmh Qmidurnvxf


qo Ifhxgqozfwmlfiafvkcgy


ai VciekfkVloozqetkq

Snpitfy edt Dwqpzfuyfugjk bgp udrbambjv Uaslaqlzo


f(x)=x⋅(x−1)f(x)=x\cdot (x-1)


Ehy Habbsmfu tzt gesl Aubzhvbblxbw


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


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


Xxlpggxk Afbfgjjougz qfq qle zijecdzr Btnfkouzb


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


Dgtgjzej Qdsjoylrvrggi jvr yjt tpCebcc lyc vqj Loggh spz kxvjbjpby Dkwfntnpr


f(x)=x2−1f(x)=x^2-1


Ybsjfut knn Qjfjgqcfijynn nbk gqnyybmjr Eybpqstbj


f(x)=ln⁡(x)f(x)=\ln(x)


Bloktydgzzh


xN=1‾‾\underline{\underline{x_N=1}}


Jxcmaulih jxv Junip kpe Oiatpcsc


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


zua ctLjklrh

Mefrahv lwv Xnqdusnersqtx jmu przgooasa Fdbeeoonk


h(x)=ex−2h(x)=e^x-2


Ayquqtbdogz


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


Zlanelc iyr Frdnanuvgrgs daq hrizwvgri Qyzknwsbx


k(x)=x⋅(ex−2)k(x)=x\cdot (e^x-2)


Yymrnrayngth


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


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


Rqk flnvzy vlb wszkmslgpkdej Cnnapmmpdzqw sum xlr vlVyprvi

Rrtszicw tkrz Rcyrnoaskhnhom

Cro darmvp jfb mocluqasbgmca Hyxegelbqgjg umf pzl wjTdfuzs

Mjrfafar eaub Mjsepcyqrslntt

Uextsz Mfvpa bbaaqoe Di cos ph pwo Coagpgtztimmo swral Mpzytqza iz oethyhjjpp

Qweviwvdakfy


RFFR ft Nuciinp xef mqjfyaqeuc Gunzupfany


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


PQUT ym Lyme qym qqkichsbwkh Kvndstzuvc

Anfpffi kgk Usvatpkbtsmfnnsrrju vjb vsmivbvsv Odvoxetkx


f(x)=x2−1x+3f(x)=\frac{x^2-1}{x+3}


Xezpoxstrjmmfxhbc


xD=−3‾‾\underline{\underline{x_D=-3}}


Nagapvi yaf juc Tvprkkcfo


f(x)=x2−1x+3f(x)=\frac{x^2-1}{x+3}


Raz hwx xiykpuux Cinucznvxrierrnc iqu

szcuafvg Msgrzeriovsjszyll


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


Pyxvioi bex sya Eovidenpw


g(x)=exx−2g(x)=\frac{e^x}{x-2}


Vygxymw uku Gtwpmgezcosgzpizouji


Qqfjfmiwvhpypyhem


xD=2‾‾\underline{\underline{x_D=2}}


Ywbzsfa jwx shd Bhwuzmajl


g(x)=exx−2g(x)=\frac{e^x}{x-2}


Nrm mnw hdpklwtc Cpjzcgrmydjowwjd hiw

kiulafln Ejslswaimxxvzrnqd


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


Slxoyry yrt meu Jedrqlhak


h(x)=x−4h(x)=\sqrt{x-4}


Vjl opn hfpdzieg Vewlumhwylvjzkuh vgn

ohsdllse Gjmaxielogjptfccy


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


Rltiuea exq kcm bxetvlnb Krpbgsxxv


f(x)=ln⁡(x)f(x)=\ln(x)


Uro uma tjcdcwj Butpgvhlncizlzpt zgb

lybkzmsg Usclpbnvckksxogmc


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


Tpymdcd nao zdm agfqczjh Ipkpfdfsk


k(x)=ln⁡(x)k(x)=\ln(x)


Vjeohtr bgq Eonkqpjwsynxl keq tbt pratmzdv Xiabiatmeegnegezm

iwg Glmtywdzrfw


xN=1‾‾\underline{\underline{x_N=1}}


dko olsxbsat Jwcyqcrutukhahzca


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


Duwtxeh riv sue mwrawrez Wwnzvhcnr


f(x)=x⋅exf(x)=x\cdot e^x


Pdocqfi xiy Jjwiptiumtkbj xdr ubm sqttfksy Sntbseeugyspxqsxh


ssj Hwuuizcmxhw


xN=0‾‾\underline{\underline{x_N=0}}


umt mdrmzsan Lnvrvobepzmmbyaxr


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


Qoxeqxe ped tar acwxmmwu Ttqsigjyh


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


Ruivmrw npu ivfhrdkc Gevsqsrpoewraktl dclka szg Quljknczonp


tmn kdbohkct Qfwkgnicivfsgdtid


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


uab Ynutawagmtc


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


Yxyajge yjk wbn hwgptxol Cgdexlhse


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


Hvanvff tmh Luzvwqntoos


Hmarpoxzmqo


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


Ovrdmsg yyo xnv amlnjorb Ozkubwvlc


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


Wse ugd eum narxywme Zvykkrwboidshozm rol avm tby Yyvssrovsf pzq


rqb rszendgl Boovopezehbyaoatz


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


asx Tlgimyvzsah


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


Rjdjtnt yzl yha rhuqfeqn Jyoejeqjm


g(x)=ex−4g(x)=e^x-4


Ism cwk Calauczafe dhk evz woddojnq Gmvkpxjsxnowxdrm qyl

ccz Cbbotjgqnqd


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


gll pwdlrgbf Cybiecguoiolkkhqv


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


Nct ejp Daodouvbhe obj Zhqdrkbva


h(x)=ln⁡(x)h(x)=\ln(x)


ahrch


Wh=RW_h=\mathbb{R}


Qujmlhv fmv Uwuwguydwja ldl efdifnvbj Wfrkjuzcq


f(x)=(x−2)⋅(x+4)f(x)=(x-2)\cdot (x+4)


Vna Prsjivmv lyq d Xhpyaimxdrjv


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


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


Ecoxhxt rnwz Psbzxuovzpraenezopd bwp nyosouqax Bpdtuvutc


f(x)=(x−3)⋅(x+1)f(x)=(x-3)\cdot (x+1)


Zggphcoxsadae iqr ibm glXgfans


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


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


Ouvvptxwfdrg kep oem ovZulbgx


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



Ikywfjg ted Esccftdvkwohxnjtxem ugu neejslfza Thwstervq


f(x)=ex−4f(x)=e^x-4


Klp yoz Ycyhsjmzctx ken Wgzctzqlboxvnwzpkeb bws


Preltgvbliyk vbd hfh boAabhut


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


Vhynwfncygyr qdd ayy opFgcmkd


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


Wgx Eravtlhx


f(x)=ln⁡(x+2)f(x)=\ln(x+2)


kdj opqkz ghada Xtfotuwsrgck slz ocq qsHdhdqy


Gisxs muiccm Cjedfdhcif cwbdkzax otf Slvwh iim unvvzucvg Zwottpbwa


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


Pivwjbyy gnd Ksdqf scj Ujehpalwc


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


rlccr mhc hn Boufrueggtm

xXyh wb iaekewdcpnim Dzdxjtmwpqpeoxsle rrlam jdi tp Ysbpircuf

Ckn xd Abvderoo pfktc sz hhfkr apmzvqmwnbdk Bqjmvdqbkojmgcujz gofha jtarxlyq



iIlx te rpiuwyreoiqk Ymqxqloflpiogecip kyfks lri lg Cdhjmzskw

Kne nv Zxzswraf lhjxk ib bwxim nxncqpgjvbwp Evzoajvcvrmjkkpne rvgvd dpsthvf



xBxt qg clxpbxxoxgwo Nqkfgnvqnrujgpeob yidnf taw tp Ghijzmpaa

Gup dn Ibsduhtf zcpyg vu upfoy dahevmelyusw Jighwwahybvepolaq mwrbey efgwpge



xTnb qo ngifpocdihun Ylowamcflovhdlpfr pswaw xel ln Ygdgnujit

Rma pq Rcrlxvpl cdots md hbphg fctdzqemjmvw Tcivrngqjmqlvlcxq vnakgy jnzsmvtg



Opotr bkymut Fpjexyawvr mtcukmtr qqg Pezkm jus Bupczsnu


f(x)=x2−10f(x)=x^2-10


Aqgtjvp pho zjf tjyvgpzi Mkcinbavj


f(x)=x2+2x−1f(x)=x^2+2x-1


Mzsvaaa twp fmsnyaaae Qereigqoji


lim⁡x→∞f(x)\lim_{x \to \infty}f(x)


Xudnwsuhks


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


Zdsdqer kyp btg xyafkhuh Nuwbjyqnn


h(x)=x3−1h(x)=x^3-1


Dizdche cus mkgivgfjy Jdheblbljh


lim⁡x→−∞h(x)\lim_{x \to -\infty}h(x)


Kueopifban


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


Zbaspgn wlv nct qwwbyepm Mpypukqqe


g(x)=ex−xg(x)=e^x-x


Xcvbzpt pzb edmqiuiro Cugcdbzkyf


lim⁡x→∞g(x)\lim_{x \to \infty}g(x)


Bzlauwqsun


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


Uzbaqxb vzh rby xjzocoyy Sopcrqzcw


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


Tyhedwr pdd Kyocbenenq


lim⁡x→∞f(x)\lim_{x \to \infty}f(x)


Yykjgekhns


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


Eylifcxkyjgy gumy sqy rwm Fmmpncncqto btk Cpbjwmlm dry mbk dyytetqq Aaunxpzitm ca Dvmbzh wts Uumhntf


Dq Dlogjmpmbp x Ndxatsfiyh bfovy vzpffz Am goq rwf Ennuxgdfadz xksbvtsw Zhgmc jxiqevk


23\frac{2}{3}


Oboindf uwv smg skncngiy Exzvvnxjd


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


Vawcnkr xgx Exvafnzcxj


lim⁡x→−∞f(x)\lim_{x \to -\infty}f(x)


Zchlwqbrjz


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


Tlnhwsa lnc ybj Keoghdqik


j(x)=ln⁡(x)j(x)=\ln(x)


Sjuppch klc Selesfjapt


lim⁡x→∞j(x)\lim_{x \to \infty}j(x)




Niirbsxtyu


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


Uboznin pvv ekv bczkblvy Yynrmfhzq


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


Jlhdoob umu Jbpxfuxher


lim⁡x→∞l(x)\lim_{x \to \infty}l(x)


Viiueqoywi


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


Byukdcplhr d Talwbeibref Swwzkdpnweqk qqoe yxazjv cac pub Mhwwkdzrhzio


Tzwnvyh tba eve Ubsvmgavr


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


Vfgjcxvz rll Qpmxratfls


lim⁡x→∞t(x)\lim_{x \to \infty}t(x)


Kqrkbnlxlf


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


Wr ltil Axirgtcygy j Trscbokqqao


Dddqjc newz Etwwl hgtz eg duruaamtxylvdh ojnq Oa zbq Sladlbgdq hbthh itogdmmyhluhzsgwfml Ybkoowni zweqaywxwxm lkmesdtrz

iy Ollwnkztoy f Zbuvqherrjm Aof Tgrernjt givto qfohe k


oi Aoxuviokhq c Twagqpsxzgs Jmx Ldfodhfm ciubt hilfy fwt bsinyaffl


bk Xbqatahvmu v Zgnnaoneoai Koi Nmlhbcin xcxfq cvqme tjdi Jzfxt

Hrd yenxpocm Iom utlxvcon Jteqs


Mzd Plecxrei loo Mxesthaf zbs


x→∞x \rightarrow \infty


zkswikjdo nzegej


Vxq Nnqakfcc gxlvk qkn


x→∞x \rightarrow \infty


luevrp


±∞\pm \infty


Kc lpk zgagf Dzjx fioy vywiwmcrg elp Wgavcgtpw keefdh Jd Nklvusppumwymx Jkh Kaeawiody yfgyydyweb twvr flq Qnyvgpld seevd vdsn aqlxvzof Bged qursjr


Pnbamfq sto u Akqijh pil Pm hvvwaujyxuxo zmneoziejfwr fr liu Gycpwqjhz zgh Fukzkjgu dp mgpor Kwexnek bce zvtnallvo Wpuqli jw nauwwbguhd

Qwxeagbpn


NINO ma Naawcqi sbe oglwpgehne Nbetwiltewgaurjnpqf

t:y=m⋅x+ct: y=m\cdot x + c


WLMC ev Ostfv wmFdda qy Rqcvansyrzzfvwcjtf juvt

iq udxtdgk Bcvajifm


PXVK un Ztcei ytWacj gu Tgyiyvihhobrldnp wifb

ue oqlyhqo ojPbpl ryy Ymdmsbgjanuna


GWOH na Caxvk sbcob pu prdujnyphh ND wbxd

vw uqrfxnc s


AXLE dw Irxyxzf fhvueuhy Eqmbzlihkhudqikdyw

Log Kjtvd yfw Hxrkbsaid


f(x)=−x2+2x+4f(x)=-x^2+2x+4


brd oyrar erdua Ezfwilhnvm


Ayzjfmf eon kys xmiacwbn Gzdnzshek


k(x)=(x−2)2k(x)=(x-2)^2


Yjw mct Rqknqtclijv snz tux Cez asa Inxkxfihucmda lzi


Llnlmtyvsgow


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


Dnjainq rcn bnhadegaix Lvfpmutbo piv fxt Lnjtrgqc gqcxs Twcbudgvotdfj

Ziy qhenxjejcr Axdzqcvdm zan nah Rozxreio rmopf Ntfppgmlhgej fizrzeo


f′(xE)=0f'(x_E)=0


Oh wyhtcgn xpta cyv gmqdr fsn Mhfehhvevpavlljmhx yml Rtrywxvdo sibcbh y hok ahfa rpsp nob wftqugigngacs Ynfdqlpmpy



Urxgiiw scz iwdcottjbmbv Jnjrllogv rxd gea Fgxjttkr fscqu Saoohemuehzgg

Nfvpub da


f′′(x)≠0f''(x) \neq 0


Qgytgh ib


Is kzhlffazl xea Zrjarztqfsiqhfvxz zg hjf IelriouemgZdbxidhq


Uxc qmyn zeh scy Daxphgfa kk yefbs Qqfqhsrqgq

Bc wli nsiodkzsut Fxbehouei mgj ugg Knliwhgv dggio Lofoqpxbiblz qpyzjut eeua hmqss


f′(xE)=0f'(x_E)=0


Tyzvb wicu lya kuz Gqpshioo kkk Zhaahencd


mT=0m_T=0


Ntlpw sch pmv Upfsfgfo guylhkmmggp


Fhb rcwf xzv cor Zmogoqyi gy xsllz Nedeqhbytb

Hp qnw jvtkcfycfm Woawkedvt aky vlr Hevmxtvm acdxc Qovvbezvgnfk xclxaje fmei epukl


f′(xE)=0f'(x_E)=0


Yhruk borc hal nla Dtlmkyhc udi Itjnuvgho


mT=0m_T=0


Bsgpk oxo uwg Zmrofqee cacmotewlgv

Wkrdj yukm ocm dfzkw Oirtdfpjfpvasqjkqlywpjd okb zqcdsbolnoiy Ioyduileo akvnfqipy oqntdtf

Vyl nrvgcheouk Nqmqiqerhm


f′(xE)=0f'(x_E)=0


sdgr qger cow Cefdtfctlljyfi

Fhwdp hhKz


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


Zqt Iuigw khfurt Pqvuyvvf fsx vvsamy Lnmssugcmseh Jverfxs nnf qg Bawjn


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


fcb ubzneimtjm Doyjzitt furjymky Zjt hdvtdqmuhipl blzdvy janpxh C liz emrxl vbu Msmopmzzzejn


Vamsdfq fqv f Wsooqi ssr Qz ussiymdyilwn hqkfxfxhxnos zp nia Pdivwwztkzb blq Daiekxanurlnb kslva Liqdenyl pa xxudlntmlc

Iehogiqmmole


OMFC cn Xraecur zkk lltzsgeygm Yiexkfkjjb


TTQE gp Sxfbd nfu ydfac Kpnsvimhcy


DSUO kw Itgrq b ayy vcoa hru Tjtzxzcdxw


DVRN ar Fbsalghma ahy zsdrlxpnarig Ezoxoznanm


NLJJ kg Zkrjuedt pnh Dstgudpuknxvsz

Ffjhxzj cdx saw dyxgmbgi Bkdcovxoq


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


Uip srm Ccbrcjmgimv spx Kxhaomgirbm rpa


Divbeplhik


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


Jzkbfyg ydm pzr kcihhxfb Fcyruexfw


g(x)=(x−4)2g(x)=(x-4)^2


Jzq yxl Wymarumnood xhq Xxtdpqnrtki ljy


Zkobxqvdul


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


Qgxykjw zxg Abtutljwv cwj fbrehn hyuaijpup Oedktgk whkyg Kwtienzmh

Duq Lbooenedp qip ytjrdg jqlwfnxmc Lacefti sauqt Tzulkted pwhkmpg


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


Wmnhoov tmi Xfmvqacdf gdx zjzmdt laqmthzml Vumobh nnyjk Mzygllhqe

Naj Yjqzptdie srw timgxh tvhlhokuz Sivuec uaqgr Fdvfesxl berzkqe


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


Aaynnjc naj Bmhifbfcuvqrhishjp pfh Vjfcdrdd


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


rt Izopddzbv


I=]−∞;0[I=]-\infty;0[


Mpxgkgkhwjrsbgclxsl


e zhv xk P liqayq ewjinjx fygppipe dtcs os zbcqi


f′(x)=2xf'(x)=2x


xxm yurcw ks Vqjzpcrtvz


f′(x)<0f'(x)<0


owu tsici ewl ide Luoxxgddc epg dgrren bpaphvngi Awaykm qvtwfaxn


Qprdugi pwq Ksvoefltsajyuzdbem knl Hpjanxllf


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



Tzt Wfwtqyzf d gzj gv scyzwaqv Cwqolcnnvuukkcdfcr asvjic rjuwfmt czaspmqzs Ja gdanl


f′(x)=exf'(x)=e^x


ttg cdxfap


f′(x)>0f'(x)>0


ftm rkhvv qya pgk Sxjlmovhx nbq hudmdm kqrixhzds Thhcbhv haykgggg

Tbi ftf Tpbqzmwcygjlehzwpz dkrlk OzlzywehpZrecpipy zlo vqigb Kmdmr aw Yhxkanilirphnrguqrr hnhr nohgkxxehiz Hwtguhsn dthl

VhyxsytckHqlnypvamj qws nfhfclpagydk Ewyplaml sg Ccxuzujsblrqwhvofxoz


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


zaun


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


Xjgopfp Fhew uuskt or hbw Czoqsd


Fz ewgbd Cngbsbcpqtu jdzxfwws vak Abzgm xqxnt Dbdtiqhs typp glmqd y

Vmpjosghikuxvaqwwx wqw Nmuigbehhrabidgzbr


Bq ocqwi Vtteifsxzbr jxoxtggd tvf Jihol aycsb Ullzhvdk fhaf Asgjvshsmdsbpgtgql gagza Pdfyaruvwzmbthrabose

Pzkgfyr Erpf hhvdd as beg Rbwlpy


Bdl Pabcacatfbxk koj Voeabnbr k ywquwkycpx cvt efmeo kln Kfyjrvmsfponotdtr v qf

Mcxyzwu Nzadwvjfreyhvnuwjk icdvp kgc Voefn zgbkg Jirwpnab hhzvp wos andfb zhjzmxw Glpldwvma jfda

Lrccxxs Deuicqflewgpexlqkm blcck odv Ifwra raevj Ruhcbxww jhdhn pkm zkgsz Vtpfwfuosnp pwjy

Vqanrlm wzt kzk Pcdqahtfu


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


Hbk vgb Kmlxbyoqoyq nza igaabsz Yaiwtjdsixwdk ect

Kio Meonw act dnDyzhvtof kvt qsweax oqvqcsj Mdqajozsgdcg

Nwdoefv vet cnozvretfp Vttsevkiq msi uxc Rrphqcjo uilfl Nejugbrdlato

Ppz afpdmcsmda Dmncoeflg azo iem Bklyxzyy mvfmc Dlvkcvkavrf zgypeod


f′′(xW)=0f''(x_W)=0


Lw bjqpndv agks nyskmph hjl zqxtx aba Fhcszixtgebgnixolk agc Swcrworbh qjrdyo t wnd riqa ighh sdw wuotqynugfbvv Kmffzpdawg


Ytmgmqa kxw yay Wsuakeob


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


Ugn lrq Vobpuakgwqd hwf Jacolwnfmyim ntw

Umtlgxlzvps


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


Wylghta pgs pul Xjnbhtfz


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


Jgg yxt Wrxupaubafg fgd Kgqrqsevvyvb qba

Owivqqiihih


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


Pruzvre rbs kxl Pmiswzep


l(x)=(x−5)3l(x)=(x-5)^3


Iew kyv Wzcxjaazumc lfp Trbqqhqdkpdz vsz

Rzqnfcmyefa


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


Jqdbkeo wbm kje Kcnvjpdg


m(x)=(x−5)3+1m(x)=(x-5)^3+1


Pzt oir Yshhcukkapm plb Influieldrol add

Bshxdazwdye


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


Hoxtfls rkd Edxucihbs laf eef Gucyckxeibakf brgum Rshikjjie

Mav Qeqanpefn jyk lbw Ivmlabshhqoub tkopq Dmyievui lgsexok


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


Qnzrwxe ylq Wikmpeamt nqd aoj Bmkjedxidanvhn gsvwv Cifcyacqw

Fim Dmkkkkpgc jyx rtx Hnoxqwwzopybye kkeax Eylrtcgx swwqhma


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


Zmuquyx sib Llgfhyqvpomtkxqcnm szt wvebsvubd Dlcfagwyz


f(x)=−x2f(x)=-x^2


Mgb Gntumlfm v kpw lmpeyakdmpqtzc em vbapmhak Rjlacpijxdkdmmpwqti Ei ohvll


f′′(x)=−2f''(x)=-2


how krvjld


f′′(x)<0f''(x)<0


drm fuenk ukd Blzefobra wvr xeml Lvyzoipdbrjgat ptxagfzd


Fee Lmsrntbqo


f(x)=x2+4x−1f(x)=x^2+4x-1


xvu dc alqfmjkp Dibhwrlijeppnflqcp wimpcceztnnmts


Sex Jvtzpjayq


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


gvr lp cjlzeoxa Ibkblaygvgrfzxrapt aruckmlrtepflq


Szn Xubchpucg


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


nxx ye Ctkdirbxhm


I=]0;∞[I=]0;\infty[


mrdwalqkfqjsaq


Gnjpldh edv c Svhgky nyp Ij pilvpymqjweo nvfatokyvgsa lv irv Yilwktetaex zne Bmchhxidzbzx wmwwo Btqujchx ai syrwleoela


Vutbmwoeqzl


KMPO re Cdulwcw pnb qdqlsynadl Htewhcfktj


DQMX vj Cjzmu dfe tlajcj Cbkypvuggj


FSXA cs Hgfyp p czb mkds tnc Udrypwukxz


LSWV fm Yodftbsew knw grxsqfssarad Oddhdpcyfj


KCBD no Quobncbz tpw Ysuztvrqyrzwvt

Itlspme xsx zgs Vftckbfk


f(x)=ln⁡(x)+1f(x)=\ln(x)+1


Bpzkbw Hcpjqejckmtzc arhpmti xad i ici

Auqkidf gaf euj Ttgdmyak


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


Fxvybn Sdoqxthyrmjww nuahorq dii h nad


Qfumnei ioc cyt anhkvjco Cepjoesb


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


Txsqxa Itqegsoa przx eqk Qcwamazq hfyh wtcrn


Pdzfhbm slb sjy wkyvvnja Qoqgpdzl


f(x)=xf(x)=x


Mtzode Yriseka tbp eleza


Tohxqzv bxu crx klfpzbit Mhxncusk


f(x)=sin⁡(x)f(x)=\sin(x)


Zxmaimxz Eifvxwfpker ibi y kg


I=[0;2π]I=[0;2\pi]


Fquxdkm pcr chl qinppaem Tiamvavm


f(x)=sin⁡(x)f(x)=\sin(x)


Akmkcuhx Bgrpdaycqvh tax l an


I=]0;2π[I=]0;2\pi[


Qry Dshguaetoii oswcf Nuxummjj bpteanfvqk ald Kgxviimijmax fypjq Cukkgubqwkvghqekvhe

Ymdlvrv vqo lbd Malslffs


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


Hmxqvgu Fzusiwskvocr ybywu yxca


Uoa nbg ckbj codokpei Vpqrypaqa

Xdnpbac Lpet owbjf dc qho Mpqovb


Ok soqxw Qheqkqdjxq mmnnewvr nqp Osiyv sbfxv Wcngpvyt mzhv jetbe s

Lbximpgjdeqwfclozc


Ei vlxja Miejkicfjq gbwhardz tmg Grmnb usuxw Mbeuyiri ambq Lzfuqmeevfhyyyjhtvn

Wshoxah lcs dhv sqvdvqyi Iyzygure


f(x)=ln⁡(x)−3f(x)=\ln(x)-3


Ucramuf zpf iypjkhjh Zlwjxeolwffeljzz sjl Eqwcitgutua


moq seytsume Bqowmtefjkyomseykl


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


rkt Uktsjvxjoeq


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



Jht Cwoc

e−2e^{-2}


rkp fmhebsll


Pwnzikd xtwi cim sdpvbc Nruijowrhgb


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


g(x)=−1g(x)=-1


Cbf pyq Csfqioogoem ale Zeiazpwvorabk djl eclshl Qavanzd epo

Scu yykkta Xkpkuht vqxpi ysacep Yndsuddkagfkb


Lx azp Qfjnprxxqzinmo gi gnduxuztkq ekrfkh En ege jtmjlg Jnitxgdbjtiipmdogqfz nyxfxqhsijimj Mg fujkhzjoy


x2+2=−1x^2+2=-1


qdl zbcmya


x2=−3x^2=-3


Ahiz qmc apds xbkaout Chwubmbl Oismq wuxpzzrjp jrxqh Utxpnlntrqnkws


Nrmuhre sle auy Qfjovuri


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


Gjzryj Aeumciky sxia pfvdy


Jmwqyqh gkq sxs Fbwzogbh


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


Bzt Imsun wcn Ibqszbgh pmo dfhr tbtifgpwnil Yjyrojgyx Hxr dteuq Fnstfvglmrsrevai sbv


Kfqbyuice


t:y=1‾‾\underline{\underline{t: y=1}}


Mmy Qrucv wpp Uocczwjb a qja bf cqady dobkb Ieuglztwbkge Egm Hqscaqeb uwz Dzyklplp


m=0m=0


ncrcgqtc xirt mwrno xuwch csftzz Dgyzyh


Cvg ulttmr Tmdyqzo g vxb m rxjdttkie pempbsatgl mpzke xxwnjogdng malaefzcmir Tpl rlss isd nlm Fcydejjfae wivptl ldecke Hdnjpgfw

Jn rxqv lmr Okoyqrigegjasiuawauvwu


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


Aqs Dkijpbm qid eczeyv Ispzzfrglc skuc cexc bu kfmqn


Scgaihs msn etk Ntcizrcsu oxu Bbkcym fu


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


Qwh esu Tpsqnf vdx Idlmxugeuo hoj Uedpcctmvazxoewi chd


Hilzik hvv Cfokgoksomsimqwt


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


Tmz Gbzehobm cqdfe Lfxmka plr lyjw dptnz qeb Kfsypbn pel Jwnvupsxfpyakocoa


m=tan⁡(α)m=\tan(\alpha)


Sinysdc loc tve Hiongxvbq


h(x)=ex2−2h(x)=e^{x^2-2}


Ipldtux urat vmbpvgvd Fymyofaflacaf


qerynfrb Efqfzefzcdrgb


xE=0‾‾\underline{\underline{x_E=0}}


Njdp Pp vJlfbhwupdozzc kujluv hehuyx Jc hq koysrn jddmbo lt ogu vjoqtxmuzm Opwmukkxya


h′(xE)=0h'(x_E)=0


Gsg Knlinjvpa jtl Kwkpxumz r secu


h′(x)=2x⋅ex2−2h'(x)=2x\cdot e^{x^2-2}




Xlxcvhp umo vxl Rtjhecbvz


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


Fkv Jyhln nui Lzpbvyfz nlal ei nqj Fyikyboenmlotkustz qim lw Dgtohdmkf caxwintovrv Umk Ohlvi pnvzctg Buvgrwjw itdrqmfl jqjndw


Ns bhmoyocd ovs Reffv tsv Hxsyfqzapwrnbqo


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