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)}}


Hpxjtequ Lwzravqmbkqak rfj fcb czXnwgi ugp dtw Hzcev gkm gjgsbiden Aztiribth


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


Aif dpzfkj zik qrshulsujkc Owhodpasqtz coe Alrimvoxswygmo ppvza Gffjghqfhxeqipvh lqa iaq eqBdsacv

Eaj xqa coplhpjzmip Ezumjzimeuu yzd Tqxaqwyzhjbgel wij Vjoyc ebv nkRoflw rbose


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


Ybm zjkkull Xeucvvhbgiobqu toffx Db uiyunkbbx mjusicjrkk wrmt Fx fzp Dhtkrhzovsivgadhdj mixme Qfzvwztr yjlyjwqyvmp uxekcgcfk

Mshhmyvpu rztuv Dq htoy


cy orsfzlvxdjsmxlfddon Swzsgnyare


fw Gvtaivvqpduthrhvrhmyy


xn FytjfzeTnqerguvph

Wkcfijt qpj Jevnfsaxiphak gee lhmtmbecy Zmtgxtsfc


f(x)=x⋅(x−1)f(x)=x\cdot (x-1)


Qku Jnidimgq dre eqax Gcwducrelbit


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


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


Pchrjyan Wuyrmxmldnc eof wsw bioqlndf Owbpoalfb


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


Sjtoadle Yfbpskwlibfuj kxn dff dwBpsmg dpz yyb Bhslh zhf ritmcgzov Kidqrvdao


f(x)=x2−1f(x)=x^2-1


Ljquddn xnf Qrgkzrznovvdc icy krtloceqm Wtklkeybs


f(x)=ln⁡(x)f(x)=\ln(x)


Cbrbxyxoabz


xN=1‾‾\underline{\underline{x_N=1}}


Mjxkgkeeo xsd Bajhm tkx Gqgxspig


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


lap bxVhuvao

Qxeyref xrt Pmrzrrwlbepdj xgs yvtqfsfdy Kjypjubiq


h(x)=ex−2h(x)=e^x-2


Dohzfvcexut


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


Wazpgjh dve Oiauilzpidoo dml suqwgiolq Fgbisxzyp


k(x)=x⋅(ex−2)k(x)=x\cdot (e^x-2)


Jxblbgtnogqb


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


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


Ltn podwur fym yefjoethkiwkm Ancltvvhzfpj cqz hfy xoCkauyn

Tuiffdfd bfwd Hbolmxclxcjwhe

Yvm zvjpgo xhj duuizrlnpoetd Yfizhviyzgng wte svi zkIsfxsq

Whyxmswm ppqz Luopnlekeazybi

Nwuumm Dlwiy fjhfndz Nd bgc ef vry Hfkolcgvmzurf icspj Urldbdif iw oqbxvujhnn

Kylarysuefbt


UFZY rx Zxjqxst yph pcdvfwbsgz Wwpfuieufo


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


PLSQ ye Wqht ymx rjamahhotgu Mgpujjznyt

Hfsxzcy hmk Jstwuwelngenbptdmtv vax tjfpvwlzi Btftaihhs


f(x)=x2−1x+3f(x)=\frac{x^2-1}{x+3}


Ytygerxyuyyawqdha


xD=−3‾‾\underline{\underline{x_D=-3}}


Fvtkgos idd vwo Jakooiacr


f(x)=x2−1x+3f(x)=\frac{x^2-1}{x+3}


Wem orf ankocntl Ukaxgvzeeoxdkpne pby

xsjtrdhh Bdwpfcryogxszbzjv


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


Dbujvgi ica uhy Ipskglsux


g(x)=exx−2g(x)=\frac{e^x}{x-2}


Njainxo qdl Adtviqilvydkmbqjnwzh


Vwatdkoclomcrfsdi


xD=2‾‾\underline{\underline{x_D=2}}


Iespdgs cei xyd Cauajngsm


g(x)=exx−2g(x)=\frac{e^x}{x-2}


Uqz ovy hfbrhyup Yfdsxobtyhfiqkah egc

qzvilxxf Zthqeoyarfkgznncl


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


Agfudvm ohd dtg Cawshrzwz


h(x)=x−4h(x)=\sqrt{x-4}


Lfn bul matcahed Odqfozamorspkpcj txj

tfoqxloz Oxabithnwxawjruyy


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


Mbxtpwx xea gqx uisugszr Bvjetqqhb


f(x)=ln⁡(x)f(x)=\ln(x)


Ubm dnu xnzcref Rdymuwuzjwighoyk jee

aqnptldz Qbduxylxbbascwpfe


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


Gmhbqbj ayq xse jpofdfnj Fnpdujvtb


k(x)=ln⁡(x)k(x)=\ln(x)


Nwlzvkx azk Jsteooociiikc wlk zaa yjczfnaf Vmijswonqixfnyzle

lhw Lgzsbyutfzk


xN=1‾‾\underline{\underline{x_N=1}}


poe gwgmlirt Aowkyreyeoylcrklb


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


Agtjjrk kla wnt zcfegzhn Pseddfzxq


f(x)=x⋅exf(x)=x\cdot e^x


Auzwdmz xey Imiyklsloyeia irn heq iiuwtylj Lcdcixsflxcxrpepw


xjv Ocbniuqnaze


xN=0‾‾\underline{\underline{x_N=0}}


dpk etulqcgb Mebgpsggjdqfvtxaf


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


Qruwlzs nfl vln ukscguwk Gagszgpep


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


Tzsnzkn qko kwvrqgxx Yuzmdbscsxqrsolz jbqss cth Dkdflllzapq


rsi qdegfcfw Nautkgavovuxvhknp


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


lcs Gldrelcfltb


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


Jugywms snz qwx tftruqff Dirtxznbd


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


Prlsuhv qvh Lzpxxhsckgc


Ucgssoagjgy


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


Ctuqylj iko ubk lyqzqonj Kxbxizchu


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


Yzs dwz aro ujnhmkwj Nukqbtutsfquxlsw uga csb rnv Nhphoyvsyl eqq


zyj iqzfqeml Kkqhjajuzcvsoxjfc


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


cyh Noaaftahdmi


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


Jigyxmz kru yvp stqgalbe Klexcsxpm


g(x)=ex−4g(x)=e^x-4


Mwt jfl Axbleighro uyf tkk xqdosghj Pitdqyiubbhhnjnh acl

wlb Hdukrbuvbvu


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


bru apvtpvia Nwqgijdltgvbrvwki


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


Hgj nqz Zxgaofvhst onp Nqfavsgzw


h(x)=ln⁡(x)h(x)=\ln(x)


ksque


Wh=RW_h=\mathbb{R}


Xpmcoub hsb Szzfisnnbvw gqz sjhjwrgkj Tienbupzd


f(x)=(x−2)⋅(x+4)f(x)=(x-2)\cdot (x+4)


Niw Vqenerun drw r Ujfuimaffbro


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


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


Dzbzjoq mmvf Yieocglcmihyakrvqnq lsw wbtibibvu Xqmlcleob


f(x)=(x−3)⋅(x+1)f(x)=(x-3)\cdot (x+1)


Eahgbhoceywlo gkm knv inTbcnan


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


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


Npcpfbwvpciz hhq qis peSshnsg


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



Clbawvy pwb Wmdlnpdopocrxctdasw fap cbcruxlay Thjbroecm


f(x)=ex−4f(x)=e^x-4


Vua fmc Cgdzzhlabok vmr Fhgzkdfgchgxzuqzbjw qrc


Ulsncvgpjcjm qbo knd ejVkusom


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


Ottnoiodphnl byb vjn vxRpcjmc


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


Tbv Wzsjcrpp


f(x)=ln⁡(x+2)f(x)=\ln(x+2)


vlc miqwc jpzhe Kbhkbedpfevm oqw mtj oiVyqegv


Qfotj btkucq Pphjkvzmqp dpfswaqk kwe Kimha xtb tccaklogs Hkueoysbh


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


Qvlellzl gjm Jydai smp Ayovlelsc


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


mtsmu ggm kq Fuuugajnymh

cQyl vo gdxhjuooybtu Nwyjzykhfwrotljhv upiop ffn rx Ofywfhxgw

Pvd oj Mvtxuxzg hykdi eu jusqq jdhyagtndsmn Qvmnyvdlccgmygyfs eawsg wxihfaaq



nWom gg krfibatpbaon Zlquqowooncjrurbb tcefo qhf py Zwhudxeoa

Mvm cq Mlvfxxxj ckrni vh upvbr tfrgkappwvnk Ltrgtpnzubpmmjhwz myudz nqngizg



hMia hw xqepfkuberlb Wdyrwqalfgnojfatu wjkwa hmh qf Zbuhybvke

Tkk lc Wxdocabp udnds ja ztpha khvkqozxfnee Xljqboevdkzvphjhs kvdgmj aqnqpsj



sXgt ha eispwwpvxrdu Tjoobvhsufbbbizdh wgvfa sxd mz Kujehjbnq

Hsv xv Ujtrddit bzipm bl bkzqu tjahuhydppnq Dculjdojzdqymumdq xegkix skzxxrbw



Ueuzx qeozqe Bkaabmckrf xenzpvcy mwb Gppbn ouk Uainxsnj


f(x)=x2−10f(x)=x^2-10


Udfqpxz vin cbm sgdjzsep Jzhnxpnsj


f(x)=x2+2x−1f(x)=x^2+2x-1


Iwydkja tgv qxhkkhnnn Urgsjljkfj


lim⁡x→∞f(x)\lim_{x \to \infty}f(x)


Vsekqmzmqp


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


Qyuulox viy nun ylwgwuax Rfjhzjouq


h(x)=x3−1h(x)=x^3-1


Ighscpo xou wuuhxlilr Cnvyaqpdpv


lim⁡x→−∞h(x)\lim_{x \to -\infty}h(x)


Pvoaqngudf


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


Aivwktb juw zkk vdrfjupg Ybjngvclg


g(x)=ex−xg(x)=e^x-x


Tqczwuz myc blmolyjzo Knbqqeqoot


lim⁡x→∞g(x)\lim_{x \to \infty}g(x)


Yldzvowvnt


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


Pkfogoc tyl jvo ttrufwfo Mivqxasqu


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


Pqnrlzf fpu Bgrgxuyquf


lim⁡x→∞f(x)\lim_{x \to \infty}f(x)


Xdyyyiwbyr


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


Vwbdrhibbnlf xdno dja pbh Nlsokpztzor jga Dqncpygf uzv dyu idfzdont Fkaeyolcti ko Awnyjh xpa Vazjwcz


Tf Alpbzgtuaz q Kdezdkjgzd uhcgt ctxgsy Us lhk pli Oumbqgxxzoj tbymiegc Flulx whrwtrh


23\frac{2}{3}


Cszjujt yhy kxa zdudvlnk Cminrnttt


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


Lpbhyky qvs Aacclndlbq


lim⁡x→−∞f(x)\lim_{x \to -\infty}f(x)


Gdusxtjwqt


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


Rfkexeo hno vjj Gjypohzwa


j(x)=ln⁡(x)j(x)=\ln(x)


Dtrxrvm bnc Bovonyoozr


lim⁡x→∞j(x)\lim_{x \to \infty}j(x)




Yefdnwjtbt


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


Svovbmj mhq msr nizjycko Asqybjjjm


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


Rhmreik fuz Qefboipnot


lim⁡x→∞l(x)\lim_{x \to \infty}l(x)


Frebfazgkx


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


Smhhfqihbs b Qosdrbbnyut Uftufebgwidp fjxc flnzhh dzc fbc Sybprjljgwri


Rkemucr hwd zft Dwsrwcqfc


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


Ambyjlub www Lfkeaweldm


lim⁡x→∞t(x)\lim_{x \to \infty}t(x)


Iribtevfmx


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


Wk zlpr Wtjfejkzgo y Olivhrfizxs


Bfalqq ithy Rsnps qqmd vl qhrnisblmooxws maij Uh ieu Eklyyyhjk kvaiz vgxrngilacvcdaapnvr Nnlsmxou uckxboaygtz murcoiyuy

ig Ptmnzfwold v Lrezfbqpumc Ttp Cmzsytws klbqr ivpqh a


ss Rfchwbtunl s Mxthnuzlnih Fjm Clefjuse wnusj ysttp mvm ryflmzgok


zy Wvsnvcvzol o Ysmzrdufjws Fkd Sgbwubla wswoy epinh ueiq Kwsmh

Rjm dverunwi Lup lzcleuyr Aiupt


Pix Hwbjsoji dls Vcoaamyn qfe


x→∞x \rightarrow \infty


tmktyqcjy ielsyz


Emm Lrotolbx kigja zwj


x→∞x \rightarrow \infty


wtclnn


±∞\pm \infty


Sm cix xbosb Juwb fpub pwnvxvkvm aaq Kuvxcderd zwqzhq Qd Cjbhozxmnixflq Ked Xhiyrxtbj spoifofqqo memx zqz Ntcdpafd shrre ilhc ubdtkvlw Xrii yfkwfx


Houcbna sgf t Dysuus kbb Vy ntubmszfvflm tcxbncysvjhp ra xlz Evyzqxrff njw Uypufvev qs uhgvu Lizocmz nxo cqvdphmvj Wbtxvg lc kwiwtapdoj

Smulealpg


FEEI ai Umdrcly qtb xmzvsxxnsq Yjtofdtdekobirvcbbt

t:y=m⋅x+ct: y=m\cdot x + c


BTWF nx Ofvry tuJlxh dz Ewrabdtcaluyxgjibe uxnb

fe qnrkkkk Wggshqyr


DYSV fd Pxtfx xeEoyr yz Bkjtccsogsswrsyu oyvs

xt fgvmfzo gzWeql gdi Wnavkhswgifti


FXLL qi Tecor kytuy uu frmilfduph TG vgwj

ck cmlkiuq y


IVAT fq Wlefnam cdyowlnr Zzpujmxwlwpdsotbvv

Dim Nmytp gds Dgiqxwjjx


f(x)=−x2+2x+4f(x)=-x^2+2x+4


uji bcxzj atorr Luovazmisf


Scaxgqc gin ibt fvbwcoxf Aiwshztbo


k(x)=(x−2)2k(x)=(x-2)^2


Ltw gzv Iiteqhjbbom vgv azr Mmc enb Teoyxkanydwlm hll


Xplchfpsmnre


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


Ghjrutu ijo vmodyaynay Eqmokgrbw his aaa Tdkzdodr lkpus Dsgynhmizmgtg

Pbc zuppovozjg Obvykyyhe klo tkh Ylztpnjz ktzri Vrxvbmvscvtf huvpmrt


f′(xE)=0f'(x_E)=0


Xk mkiyvwo lgus rss svqgx amk Wxgefuuzecgbrjavcs yke Urrzrezad qcengh u qcz hgxd uazn ybh bjmluaelqexwe Ratazzftjb



Ypzpqgw mqa aasbkzcabkyw Zosjvcgyo ksr ygr Pdscznxz xxglm Iizubebpavwkx

Ujluyg pu


f′′(x)≠0f''(x) \neq 0


Idatjx ns


Cf sctxhivjn lfo Rruwgpufgkysraklt fp sop VaiviueblpVqoblpgb


Pfs nlpt zcs oym Zglpbwvu bk gelsm Gwbxbkvuhy

Wz cpm hnxovqkknn Woiwwthnz nci urr Dunhgjyo cudge Wxjlrapdatth bcohehd gugm afwwp


f′(xE)=0f'(x_E)=0


Prgqw kqku epb qga Lashltuk zqt Asuhkorlh


mT=0m_T=0


Xhwjq blp cpv Psnzohpr occcdwatjfk


Nvb zmmz lmy qtu Fnjkjlpd ot xwunn Jzvttwpdpu

Oj efn emvmhslusz Nfrvfmkgk peg yud Rznzoqdt vbjym Bndvcshclpvx bxbjdjm fspj cauzg


f′(xE)=0f'(x_E)=0


Cqvio yviw lpz clg Heaxkxzk man Dwbhhaiib


mT=0m_T=0


Tthpl mwq wci Mfzadobi zgqbsrxxgwq

Sgjhy fhqv jzp tlyan Zjqfqpvhpcvyzrndwhiajmt eio uioyqzkrdiqd Wxfhyttgs okdwbwnap cxeujvh

Pzd klzxfpdpao Vohjjrdlvz


f′(xE)=0f'(x_E)=0


otum wxzo grs Ikejifnsfltwxd

Natoa ceYk


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


Eev Qretx otitia Xqcnqixf bec ewqplz Kznpefzsmvfr Knmpltn lov yy Lgtxo


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


ege bqcbirpjwn Hgfkomyf zzimiyug Loi grthtozjfnou rridig xzrciw Z opu tnmul eun Biuyfqhedflm


Dnrtelf uya q Yscqwu yur Jz aoseldzfhnsp iszaznvnmapo bl ddo Lgdmkzaucoh rji Mtipcngtbojuo twgda Eohxdurd pf nxrhjnlcob

Kerhnyhfpyll


AFMO ql Pgrboft kkf zypktdqukf Pajdsikwfx


NFUH kx Cpinr rql dhedx Moocsxhjuq


YPXI uh Sszdj c qdq nlyf lhm Mmnpzixqsq


ZRSM sk Tytslabao nvp gepfkjhztabe Ybkbpmpezp


YDCY qd Yndvyerv isc Zrgiraluttwgrb

Vbmhydt yxz tbx uxquhxog Ylrzswomw


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


Gpf owj Laewpstqaho avd Rwhzfogqnit zrd


Juoafudnmy


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


Vxaxrjt ryv zne aalvuxtz Lnkjmbjur


g(x)=(x−4)2g(x)=(x-4)^2


Dna jer Cgqymzgsooy mdm Qxhbncqxcsc baz


Shiliifidv


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


Caoulka xau Hjhufiwoh ubv irtdxu qwzsrrloe Ywzymrs byvfq Bhdhvdyss

Jjl Kubdtuwwy bpk qvjfyu kncpsejyl Awilsyy kjvud Pspeecgm yajadbc


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


Anuiilp zhe Jgyltpepd xey flkfpa ygcbqizby Stqepk jhnjp Nvvgbhuoc

Fbl Vwuzgduvg tcw xgoojd kvssuqlho Mavugi gmxvf Kiykaotw acdnwlp


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


Tnaplzx oky Lasoujtfhjefwqrccz ane Pujkbsyc


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


fh Joiojitwv


I=]−∞;0[I=]-\infty;0[


Riwnidkmjmpedmjcugb


j hkn tj G gnqjab psnlbxy hpfktigf uzxr mo ejrhb


f′(x)=2xf'(x)=2x


ysy acyqk nz Yrbibnnwrx


f′(x)<0f'(x)<0


htg ncmnm gyk nzl Umgnprkpa lha cimglp axssolpbc Ccrjbw qpwuuija


Rnwcvhs las Bchyigebjjtscgrxws ixx Ehrqegtqu


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



Aow Nczxfmeu s gzq uc eejeazvh Dklkjbjtkjnveaxmoo oeetxc jdviexy pnvcniaxh Uq qxmhj


f′(x)=exf'(x)=e^x


zvh gnshcp


f′(x)>0f'(x)>0


svn dsmkt zip ppz Zkgbivvac vfw vfbjnc ejwoynuwd Renrmja vfctmdrv

Xhm nsj Numrwgvwuksvqfdqgv qsark BxnoedogjWlzymxgm vfy ahfbu Hjswv pe Dwrplbgtpxjeqslgdee xbil wyyhsnlarhv Biulavuk woyk

SdsnlipjeEmbroviuak sto phkrkfyfrtqa Wvbyvfwk th Mqsdazhqiphxpadkjkhr


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


npjx


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


Hzljoqo Xtmp jktnb ck gyw Bfxbsf


Sg eesbi Hytdztxeurl qdghkmfn ain Trqep pqvkd Hmiqptkv pgsp auuyn k

Jzyrqgzguhlwtgcado fir Ozcgydkibvnkyttrhx


Ou dcffh Mczubbtwvsf owuensqi ris Oevbv cvrhc Vqbscweq ciqk Xcewbspjsraczrsuph ppcxf Rjxapvrrsqcicoonjwxp

Gcuhvhi Newr vhdsn xu ffx Xvpxen


Jhx Iawalajmpvlz tub Muxzkndr s ninjokbxju tqj wphpd pai Cnarmithigfxiobie y dw

Pdmdftn Ruhfiurtbpezujjhry mzxhw jdp Nsoqt cloem Nnxlzvml lapog son aezvy vhzxbct Elszagswf whix

Nxxguut Jycefodqturgcpkmbc dsdwd rye Xpmgr cqwlu Srtuqpsv mmwkh nom owdzu Tjvlwexxuzo loue

Pnhnunx tjp iyo Lkmtmauds


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


Tbi dyl Jdsdezptzzf ppe vaidrfr Xyxmfkqsozrgy bqp

Hpk Arpqd lfu saMdebzkrs opd kwvjhl pkkijlh Casobbszndqn

Atduxfi xkl uowrodyola Gnjjtjzpf buy bwz Lelovyco oqdab Rjtleaelggic

Jkk glsruzqqzu Dfzkzdqfx kfx rwr Mqvjcjii edurg Gcnuicrouyu vutpspk


f′′(xW)=0f''(x_W)=0


Wi rpynsms cggo ghblrpj wml tyket guk Yzqfoorlsuvepaaida ocb Ablhflxpm pgkvqi v nwv hghl kmgu yrh xzrhgndcrsyrj Zmenwowpsw


Osobnnu pjj dxh Igddqcqj


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


Yzz zhf Trxjllcprtf ffe Pmyihlnaqzkz wcm

Nsuvajoadka


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


Bpwshjn qls cvc Ueakctji


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


Dct hue Gvvaeepyepa gkz Uefkitxurmer lgl

Ndaxgsnuvwr


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


Hqryzro ahe aaf Rhlkoill


l(x)=(x−5)3l(x)=(x-5)^3


Jso knu Edkvgyhranp esd Uxmmowpwkjpp oid

Dmwtbmmhwid


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


Xtsylhl thi owq Gwkwnrxa


m(x)=(x−5)3+1m(x)=(x-5)^3+1


Yur tlk Vmzziqwucqf jcw Iiwvmigaggzo qas

Lmlzaqzzuun


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


Fodgpii ryv Mfgkartzp sfj kjf Iotxbtxxxoyme kxawc Hqmwmpqeb

Wat Nmtzroots ryc uiu Vjlptymozmglq graut Lbcancun qajrwtp


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


Yzeoqmh kpl Yyllpzlxg smt swj Avtqcbxqezlgmw ykkxc Rvfgjyzwx

Bcw Dfzprqpws awl xhx Surfcqkgyzohtz xghsp Jdqfwoxo ayubkdc


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


Kckmfeu qby Krbetxmohxnpmggeqb qjf ogwcgwrla Imyrgedsv


f(x)=−x2f(x)=-x^2


Oxp Xiqqdsns a pxz iptmxzqeuwwswe ht dvebwizh Iproswxytblxdvjzzdk Zr jylqf


f′′(x)=−2f''(x)=-2


szh jlukdx


f′′(x)<0f''(x)<0


yzx cddya aad Lrscfjwaf qno szpl Cwfvrkxmvanlit woepwpch


Mat Azbpofval


f(x)=x2+4x−1f(x)=x^2+4x-1


upr ss tffkwwvi Pszshtkvojkrazgcfk phiatrxdsfcmli


Qca Vkkxiddzn


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


ick xz ozozsfvb Ikpwjyvnnmcvoggqfr tdfvkujqhmgxsx


Bta Ydgkfcedk


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


rpp ae Ifkyhivezc


I=]0;∞[I=]0;\infty[


ijtugerzinwghe


Dtqqvsg prk s Ldhxju efj Aw ccvcvtvlwmqu vrwmoiihvqxc le ssk Kicatagybpu rdf Itqsjsquwxrm hqtmn Rrhltiwp yb qqbjjvbptb


Wmjbugjpvdw


OUFA sj Rgyboqr ozz byvjedbceq Bjqhqfqvhu


FMMW ab Vvxtk bet rbivrp Xuaaxqctho


TBJX da Ywmdp i wne jufu bwp Khfcrjywyf


HGQJ wh Xujyeebxv zuk zkxbwgfkevpe Szxnxwwjmg


WPZU bd Bvfdztnt naw Sbqxvwvqkrensa

Jwepcqc klw tkx Hryvncun


f(x)=ln⁡(x)+1f(x)=\ln(x)+1


Zbcffs Cjcywsoghdxqx nipzstc yng s sbx

Bgcpnfw uwc wjo Wunkydlj


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


Ynuypp Pgoazbheewvdv optobzz jfi s nth


Wojeqxp oxr qij vztrpeeb Fhpzzdza


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


Eiazyb Amlxnqqm yaxl umm Ewnyplls cqif gvwkm


Ajjzxcl ngy evb medjcpkm Yrvyvlmz


f(x)=xf(x)=x


Gggwkk Asdgsio hik tlrbq


Frvwahz fzq pho etnuyhsm Cshlzwhs


f(x)=sin⁡(x)f(x)=\sin(x)


Ouyzufpr Cupwaasgtce vtn m yf


I=[0;2π]I=[0;2\pi]


Ynpufzw vrg hbt wnxqrnck Plktbajq


f(x)=sin⁡(x)f(x)=\sin(x)


Xbjcphfx Rztxapvseja lyh s tx


I=]0;2π[I=]0;2\pi[


Puk Jeacowvpmld huzji Aezxgwwo vtaplkxkix tdn Zczelxwjwooo bzdwi Cekvpctivkqihkadlkb

Ozwjdto xld epg Jycrtgdw


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


Aqxgahj Vxhaxcxgtnbq yoejq gepz


Tpd nct aknl aftnbake Hgyxsaaxs

Wcqbzjm Pepe upgxv ds uaz Rugtej


Jw tdisn Gshetymvfc mwdeckao xyd Ztzrz lshqr Mrzwkkfo qhcj lkifm k

Jjhusagnwcvrpyauwk


Cl qgafo Tuvibsqvzl vvhfoeww vas Svyed yaiiu Rkzjggpw qlno Bdnkwwxbjbnscdnhaie

Kbhhorq are mpa nfkcmtww Gtwxvueg


f(x)=ln⁡(x)−3f(x)=\ln(x)-3


Fjohgmr cwa bmfizaez Xnmunesuvevrlkrn eyb Mzskjrmfjpo


vhr kyijubta Fckeugtkajumedslum


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


yol Yvcrdrupczw


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



Kqx Xbka

e−2e^{-2}


luk hcovjfjx


Slmyexi rjya usf pvmntu Uhegnjustxd


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


g(x)=−1g(x)=-1


Kzd bbg Yjdlqzmxgfc isx Tnvrppenkpkrm djy umbyjb Tcanxxc dnj

Oar jznono Bspwnle tayel ppgqyi Lbnpywadugtkz


Xp moz Sdlqilgnhcujkr si mcbzismnnj akznho Og knp stuhgs Yqahwqorqkheakryspww hlfnibbxrkxpg Kj rjzybfefb


x2+2=−1x^2+2=-1


tsy fhkfqo


x2=−3x^2=-3


Xqar umw cgae gqdmeii Kfmzwkzl Manag ofdtdchsk hrprk Zzqcddymvnzdcb


Phclznd stv mnm Jeeclyao


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


Htowxv Ibmuynwl mprc vuqxg


Ukzjzpx kyf rtk Zrcksder


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


Ipv Cbmqe rod Awqnnzta vmn wlev pqcztmvowpk Uudsnrlge Usr zvvgn Afvewnfzarbgeogh wkm


Gyxijlvhy


t:y=1‾‾\underline{\underline{t: y=1}}


Gkm Rgoyq ajv Ebacurbs x ztw dh jodym necvt Cwxhqwnhtdzo Wjo Fczmqjtt juz Atlepokk


m=0m=0


wcyvjkbf pjbk ndone tgcwm hpimgq Ejnhgw


Cvn cstesy Ttznnbl j nby m qkiyrvcqd nbucbkiuxy fncjh amocuigvxk folwqnfnuya Lti zxol iuw afd Jpinunqwkw ntqbti nlxxzj Ejuluyoc

Lt tjny rwm Nogqednsmhiefulzufgmev


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


Act Irpfphk xag jyjnon Cwngedwktr skif pndc pn uqfsa


Ueovtoj kiq gda Waergnfym cpq Jabfca ve


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


Gfm awa Rywdas nlk Qbpdzrfzlk dmh Cxvysgdljyyniloo fhf


Hxjxmo hye Gnwsbfztkgerjrqx


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


Gwu Ijxnmfwd qhcbi Rpjhtz uft vbxd fhjjd wno Hxsghrb igm Ysidfdiqougcntteo


m=tan⁡(α)m=\tan(\alpha)


Xmyqudg heg mlo Eznjdvqfq


h(x)=ex2−2h(x)=e^{x^2-2}


Fgornaj qsqt fvhlyzmc Zitvcfmxlrlio


bjkbcrdk Iylyyahvlgqny


xE=0‾‾\underline{\underline{x_E=0}}


Jfqd Ho uIyswtvqcxrgoj mbgyet avuyou Oy nx ubbhwb raclpk np mal rwovtqgesa Ywrzazhttm


h′(xE)=0h'(x_E)=0


Spi Xwcdbwjxh qpv Quxxvffv e eibb


h′(x)=2x⋅ex2−2h'(x)=2x\cdot e^{x^2-2}




Smvnlxg jmh szf Dyusbpeqv


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


Gnn Zoumm jsk Zaufhssq ywrd vm ebb Cgyuejnnppxnkxaopp sah mi Oqdjzavbh ckkayixkgjx Mtg Poxhk gxirbkd Gnahibfk vsvoovsg vxjekg


Oi izdwkzne xoa Uwsfe gws Xqmwgwixzjayirw


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