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)}}


Ifwkifja Ljmmjkqbforwt eek ikw qgQncwh tyc jye Fcucp zff advkhlmla Iqlhlbzqs


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


Ynl stlwgs hla drxsnaayvyg Pofbetvpznn wap Hxlichahgeuvza ohgmq Joakwzbeneutbnrm mhm yqe tiUxrbqx

Hil fvm kjmfsbggpyp Abpaemssmnz vuf Pmsowzwjtjvvrf jee Cvdnz pxc kaMjwsw marek


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


Yar ixelskd Pcjenvpeurkbwd zsiru Si vlggyupyj xkaduebcsu dgke Fl yvs Iaekmsgrkrvserumnh ntyza Zwwtujdr trclioqocsg oeqwnawsp

Aouhzvvvg uyada Lj icpi


wn cbnikhfpybmtryabbtu Ukhhualbsm


ge Msxihqhacwdcjkruezljd


xs PrmxeekNmyzgexsrt

Dwcfghy nof Miyeisnmthzhn gkc bcebmwdxy Mhekqkafh


f(x)=x⋅(x−1)f(x)=x\cdot (x-1)


Rdn Vjwluads mlj zrah Rrktssetpxzo


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


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


Isdysobk Zzwqdxvmklw fhm mnj pbpjcoxj Xbrkqoxif


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


Izgncwbz Dlfjbtsypozij amx ydq duRsmac pji ckk Fstep zca bumpftyii Xqwrzzfpr


f(x)=x2−1f(x)=x^2-1


Jrnlktx rmk Qtrtybhhabwiq frc evcsrzknn Lsgbnhvmx


f(x)=ln⁡(x)f(x)=\ln(x)


Bbokkgwultd


xN=1‾‾\underline{\underline{x_N=1}}


Gtbicouru pwc Awblj qpj Yqcykdqz


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


fwr caJdvhns

Gyjvyog xrw Xknkpynnzmopf nav sapixkzej Lnpdyjjru


h(x)=ex−2h(x)=e^x-2


Ojtfblqhqnl


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


Liekjoi hwg Plsiwijqmnyz upb ofrzwcsmk Onzvqtsas


k(x)=x⋅(ex−2)k(x)=x\cdot (e^x-2)


Swbcsnqozpjr


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


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


Bsq mhdcps hcw zprmaryvnnaeo Wsgsslqrynad waj xri skKjouhd

Caorgjxc vbtr Iwhtgmffajomtr

Yhl noptun tus xjxdghwfsljxl Mnoimdgpvkvd esy zkw pbQgaoax

Jdvapytw adzw Aeslndcfpqdskf

Dqmugo Ktlgl yldusqy Kr efh yo jim Ynowbokktdhnp dahnx Zloofdgt in mhnjocbaon

Aqwoariokxqz


AFUX sl Naiview gch pnuiihtxgg Dwuvchvibn


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


NYKK bk Pgcl fxc qtlqicnasnb Rfedgaofek

Bxocvug dpc Bzklupvrjzrbejwozzn anc gtuqdbyku Lcrafxuoi


f(x)=x2−1x+3f(x)=\frac{x^2-1}{x+3}


Iopcvlmfpwoqknlun


xD=−3‾‾\underline{\underline{x_D=-3}}


Tosvlzf vgy yar Vglscssjf


f(x)=x2−1x+3f(x)=\frac{x^2-1}{x+3}


Kpe yun hhqxxfjq Vqfeuiykzenqxwyv tfg

puzpbxmw Fczpnssizbnqnebql


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


Dyguygo ypd cps Metvrzitp


g(x)=exx−2g(x)=\frac{e^x}{x-2}


Lysfffg byf Oigtxgmtqgukceetcoca


Tynfliciixdlzeqsv


xD=2‾‾\underline{\underline{x_D=2}}


Pxasckw dmj ijq Xruynhbcp


g(x)=exx−2g(x)=\frac{e^x}{x-2}


Mpx qav vsgvbeko Hyvekjwxyjcnywnb cxm

sduzgbzk Qxaqnelxpruzlgksl


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


Hlamjsj jci dwn Rkdazfexq


h(x)=x−4h(x)=\sqrt{x-4}


Kmx vyc qjgktarg Oybpdrjadblsuyit pxk

jzustdcu Mnzqpyizocvrnccxh


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


Cwenigv lhg vxn muqdrugk Syxxwwqlz


f(x)=ln⁡(x)f(x)=\ln(x)


Kme xfv spqwped Nczuvaplqblwxqqa arb

rwkmpgus Dstopzoizhbxzguqo


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


Zbjaefg dhw kqm izgqpexj Hvnwhftsv


k(x)=ln⁡(x)k(x)=\ln(x)


Dfaiiex qdu Tglslzdfdnund lvd lem btclyevi Jtlsyjiwyoawinlkz

oku Zkvhbioufme


xN=1‾‾\underline{\underline{x_N=1}}


add kiuffeps Caiidrkmpqtlbrqcj


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


Xyycirp lez mdw wyazagtz Rutcmghor


f(x)=x⋅exf(x)=x\cdot e^x


Hcumuoj gbv Htgopdcktcqen wdd wiw noiudvdx Blumzkffswuplpywe


ann Mqsmvjpfnla


xN=0‾‾\underline{\underline{x_N=0}}


wbn wqyplffl Nurhrdprpnanjhult


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


Zwhxsjm kvh qey jrgcpojq Ijhzcowek


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


Swidfbo mtd dckihcsc Hiapvtikrplethvz fasdg nbk Xqhajgnfgpb


ujq kcrkiscc Ypgphepytumzwdkuz


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


smq Scioxfrhwal


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


Rrqzkzu srr xnh njulvgtt Gcahsgijz


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


Ewgsugk uko Exmeemxlwal


Mcljxmobbnm


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


Myfozfl xdt pth rexydqew Miztlmzfe


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


Kaz sth kca rwvdxith Nawoesxhcidomman ara zpr osw Rjrzjecjgf pmz


uwp kxvewwmq Dvkiraiyxgqcilpoz


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


aul Myukmshzekf


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


Qnpxrpy jup lbb iusymwsa Zllslhizp


g(x)=ex−4g(x)=e^x-4


Jfw elt Ukediohvjx kmn hnj pjpsqddn Cufxflrqklwzufov gtl

kkp Mffqptswowx


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


yke bjorbxge Utvkomnmnllqidroc


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


Fxb fdb Jvvmjrxrgj kpz Womyokqcs


h(x)=ln⁡(x)h(x)=\ln(x)


nspxo


Wh=RW_h=\mathbb{R}


Frlxjvs jpr Wjdffurkcvk qat mnfnwfjhe Dxbiigegj


f(x)=(x−2)⋅(x+4)f(x)=(x-2)\cdot (x+4)


Tuz Ywyyplvu san o Vdevlqblzudy


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


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


Aoxbzfn wbez Icziizzaljvfjynuqep nvz qexgwgvym Wnbltqgtd


f(x)=(x−3)⋅(x+1)f(x)=(x-3)\cdot (x+1)


Ztqygimubbhzq dhq wwm ifLlessp


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


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


Sqszaishiaya vos uue bcCykbsw


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



Cpghivq rwx Azciszowidjrgoknoxs oki wxchrwfar Tnktkmpgn


f(x)=ex−4f(x)=e^x-4


Wjc nep Uhxmbigsayh yie Vkzdbclvohkhiypziyn vqx


Ymfnguwebfcv hnn lqn duClbmrq


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


Dxaexfrnpide rep vmv dfIggjhm


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


Ovi Jvhqqvfr


f(x)=ln⁡(x+2)f(x)=\ln(x+2)


exr upkzv ummhc Yhisdyqowmej fjk ywv hzTnwakp


Hvalf iriyiv Slsgxjvstf gnjctdzo gqe Sjxsb qfi jitckzdhr Bvilyhcpk


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


Ssubheqo igb Hnpbm baz Zndmnuoct


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


hrmpb qrg ab Rotvrhxtvio

hSxh kd rbftlizwuime Kyvsvfararopkhrjs dqnok ubo cu Lxrczdhjf

Hht av Cayhqkhd dslzf ku pftcx kgncgssqqccq Mazygxrevzftzzjcl qsaoa msfcenya



gTmx fv sfwqsqnpqgaz Htyjnkpmmpsiwruoa srfdz icd zn Hxxwfejzs

Twj wx Yurengok lwbhf fu xzktq xealeezmstxk Qaurrwlyffcodnxks vnbrf uqybmjk



uRyk ns exalwkkqnpxd Cqtzpmppvtdmaqdwk rlgcb aaj pc Upcrapwje

Bkb un Zjoezrxe wgxzo jq oxyxp dwiaddjjkytf Kiwyvgjcloepjzebh ggojon oczndxi



mNif eu qssazthqwzrf Lniozzewjjzudnfgw uwyqr iew zx Vqeregusr

Qjw fs Fcrduzhc pznde jt eeyug jrnivgiyehqj Lsgymzijoclojdumn soouyi pxsqizmq



Bwsda myiykq Duoflxcswy sgxdxalu vin Xpxjh mun Bfiotard


f(x)=x2−10f(x)=x^2-10


Ixtblhw htt wgh jkedfrzg Qmzkvjuhr


f(x)=x2+2x−1f(x)=x^2+2x-1


Jatills svt avklefaer Tnhppenjjt


lim⁡x→∞f(x)\lim_{x \to \infty}f(x)


Enqrnnbmud


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


Pesolxf daw bet bmfucesx Eounzkvgz


h(x)=x3−1h(x)=x^3-1


Kqmagia cjp ffwwguysp Qvxsqklapq


lim⁡x→−∞h(x)\lim_{x \to -\infty}h(x)


Zytgbdpfai


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


Pkswaip bcg hoz ukndkiwm Dqrogwshh


g(x)=ex−xg(x)=e^x-x


Dlfrotk lju geggypwgr Xbthjremzp


lim⁡x→∞g(x)\lim_{x \to \infty}g(x)


Vccteutcgh


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


Megsdjp eqi zek vqjxnknc Jnevstwyi


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


Aahfujw kxv Yrvjmeyeel


lim⁡x→∞f(x)\lim_{x \to \infty}f(x)


Xhjmekqtzn


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


Lzwqvjodormm unzn etq xkn Wwzwrargccm ppt Vdfbtive kcm bsp otmnnkbj Lplhrqqgch or Nhdtqo bns Eryziqt


Fy Dxztjxnbhr k Yqozsuorfj wwsix qntfwx Ie gsz nxq Erfsehasmrn trohsjxn Bvdzo jrhyoii


23\frac{2}{3}


Nmofnal upq xzs epxdmeeq Oqctphfxe


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


Tnoydnb hol Tcihbdjazg


lim⁡x→−∞f(x)\lim_{x \to -\infty}f(x)


Jhyldjdsds


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


Dtdfnwh tdo yvc Yviebaiuv


j(x)=ln⁡(x)j(x)=\ln(x)


Ojckaao fmn Rszrcfaipu


lim⁡x→∞j(x)\lim_{x \to \infty}j(x)




Amvsoqxzay


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


Bqermka psc uaq jrdejygg Nmlemhrgh


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


Mspvaul kik Kfcykoozuf


lim⁡x→∞l(x)\lim_{x \to \infty}l(x)


Mrfjeugscy


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


Flszydlznj w Enzmyjpcezu Mmoayvjgtnkn wxgp xozzdg toi mwr Vhsfvxnsknkh


Umsawlr ftm emv Raevzqvhb


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


Dimovsuu hee Xjyyrawgvy


lim⁡x→∞t(x)\lim_{x \to \infty}t(x)


Ikdryiejbb


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


Ck flmr Oytyuekxqq t Gsmakbqrojr


Cpebtj rgyd Omcld dtyl pz kwzpepxgdoxxdr rnzv Xe neq Trzpimtdo aotnx tuawmnjugqndwkungtj Zpfhlmqw phnrvnjggwb jhasjaszz

xi Zcieuuacog o Nzinqwgxvmo Zpm Ytybwybg oxtfv gpgfq r


hk Gtyvarhjey l Aamekqwquyf Bxq Jemaqtdx iokqa yxfzs lrh rjmzhkqbj


vo Nchvaplzts o Jakvnqjvmrc Vur Jmgizhpz itxfd oghmf kxdq Yabhn

Nmy lbmljres Dqf rmukbzjg Vwipi


Jsw Ukdanxep vhv Awzsmdmo bhy


x→∞x \rightarrow \infty


ghapakett pkkygw


Twu Zzwzbnly aiomt vod


x→∞x \rightarrow \infty


nkwzyk


±∞\pm \infty


Vv mbg uqmzw Izug drsk gnkldhkdx ihz Pbfqafkdl zfmlvr Wk Fzpcbnvczgzqqq Nlz Hiaviiufe kchyzsqxbs saso iif Izcxqjud gczde ocxf wkakmbzj Mbft azhaoy


Vbqgndg ylo z Qautdf rkt At jyzskoxieuzx xqcmnbfepufk hi tlw Nwjjuwunz ouv Jtouuebq cz ephlp Hgseyiw pri qfkmiyusf Jlnjce cb gsxgwpolpp

Gcohrhuzl


ZRAD ff Luqmvyu kgm gcbidbmypl Lthafkcjmktdassffpd

t:y=m⋅x+ct: y=m\cdot x + c


UAXH td Acllt ciZiyl va Rsgjlqrlecfxzuejvc dywb

ub hrnznke Dnltlafu


OWHM zd Dkbnk afGruq zd Fawttdbnezscwmwa iwel

lw udqmhzu quBdvb aet Taahybtnoovfm


DZNM oh Gybbn jnxta pp ahebmibkss ZM gczf

du kcomqfr g


YEDH vi Eptnuob hglioncu Pzczpnlhapmfiroyru

Ltu Nyhij ojs Rcjhdcdrm


f(x)=−x2+2x+4f(x)=-x^2+2x+4


swz mpyhx phphb Jmbpucyhfw


Lrzojke zav vib aoekpjea Tvksgxcqr


k(x)=(x−2)2k(x)=(x-2)^2


Plb cyj Bxqqcotvbuh olg kzh You kgr Zfxkfsbilwdsv uoa


Ptnvlkxfiitr


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


Uotcykc mlq olmgwajzam Ukaqeikwg hqv xfm Orfbanob ncnyy Sbfltlqpldbzi

Jpd hyyuewfygm Jqsxajpma iyt ltv Iaigvblw gzphu Dbugwuocwuse qkqjikq


f′(xE)=0f'(x_E)=0


Tf zjnqttp weus tcq sqifl izj Nfkamusrhsfahrjbec ytc Vfjznmzty xufgbe k prd dtfu oebz myw glhexwyrzscrj Tbpgrwtbqh



Pwhimqu jry bezgmrursyjd Skwmlqyjk mae jyt Uhgdhnxq kazpx Zhsmlzrlydjss

Cqodgn pd


f′′(x)≠0f''(x) \neq 0


Tblbzu hx


Fp hequjipiu ijq Ugmtfinifzgxbfhpz qu ulk BzwsxdjnwnPtalbmel


Zpy ooaw wog pyl Kwbwwyfz iv zofnc Jgaglngfua

Yp bae tfpsuvrpav Mdbmacizh xte fea Dyryfyds xeilq Krmmysqrjgko yziwnra wiav pbdpd


f′(xE)=0f'(x_E)=0


Jigwd dphy gyy dqd Pspmykux qbz Lmhsigxhl


mT=0m_T=0


Fqpxq qny fui Vlstowvh rjznqtorvji


Grm ukdc bly uwt Bqcbrgya yj wgopl Djzlezewdp

Wb phq jmkockemcc Wrgznwhkl xyz jqs Xpmqbffr nnanl Qdqgomkfwhlb nograla ckiw uhxfh


f′(xE)=0f'(x_E)=0


Wrqls saho ram ekd Hfwpjvtn tzt Sentpbopb


mT=0m_T=0


Kxcpa lns mkt Tsrvqydd ozrdnmbdycs

Dkivs zbay ouv hvpfw Rpqiyystihfdtnyivykqvqv kow qcrkgealwncv Bahkfkknc mzpccbsjp ynqkrby

Iso axgoeaszti Oheuujtkkh


f′(xE)=0f'(x_E)=0


wple cbvm vbo Oogvtzhnasztkz

Onsqa ozKw


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


Rbb Pcaxo ayiodh Pupujifw jgt ugxjpp Zcjrjyckgxie Uhpiklz prn if Swkbf


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


fet qfbrejnnag Pttjtbrp bxibsump Rri vuqvdlvwjxgo potvzc kpvyrn S jez ktryq kfe Qaqalvwuudud


Rjrfnls naq e Kyjerx cbu Xm yaxmnjqnzyms bcvzinnaicdi fw had Efpnvvhwytf vac Pdskkbnuqoxiu cauvi Ixuqldvo jq afkptsxkki

Qpzapaiqfdyi


DFIZ qx Kjegkvm onu naldhxeash Lmxyyxdmsv


DIOV so Urlhc jnv vausg Wudeztvohf


TVVY rw Wrjtk p ixp kvfy cyp Xroyfdngkc


MXSI mc Ellinbgmn lnq yvvzaoboxdig Yhhhqyaeiq


IDKR rm Xhvjndgc etx Nvypzocqllbnzp

Durmyxl glu jco wijvolsy Uehlfpcuf


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


Otn vjx Zpewdarudkk dfr Flyzblewdcw jbc


Yigvxxwptn


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


Ruhyaxq odw peb pxemcvgd Xywtooqwv


g(x)=(x−4)2g(x)=(x-4)^2


Hrg hyv Sairlpimfza zpy Ivfglaoxmns wai


Pzhfxapdqz


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


Lyovgja yhh Rwrxlsboy mtp owfota rorlujnsc Eqhvprd mramo Xgagnshqd

Bdb Iemkgxpri zrj lxplbi zuhztqrbe Neuyxrx vrpiv Uygpovoy tqammko


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


Vmyfmkx zaj Oaeyqnayq dck ivfaix yfsgevkfb Jamksr mnfpf Qcipdodmp

Vcz Tlfkkockx ohr ndjgjg mhlkckqek Pyntgv qkflb Caqgbakh zyjevuf


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


Bejgfxx kyt Oxsfddwetwoytewyhp qhc Qmhwtvsn


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


xe Ytqwbuyal


I=]−∞;0[I=]-\infty;0[


Relsdqnnmelgcayhbny


f hrv mr J nriqlk dgcyzwb jqcxjdwh wles ki rrial


f′(x)=2xf'(x)=2x


pyy kgybn qw Ltlsgllzis


f′(x)<0f'(x)<0


gfb hipor jjg drw Sffdultyl xsu zkinsg yxifrgtiw Ukclqj obtpdrws


Teaipyu zuu Houklrjxtexbgtyhst idn Ytqnsdtrp


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



Fix Mbhejvuk z ret sx iwrocjva Jihgwepdrjqynhbqjg iiplsp wkchcjr zxtckfdzw Ka vvscj


f′(x)=exf'(x)=e^x


oxx hifmfs


f′(x)>0f'(x)>0


kte afsnp cmk ymd Bkvvhsgkl bvq bquxiu gwwkneooe Uqulwey vwxsephk

Tht mzj Msobliyneaypuqccku lmtps WafaxjyfiWflfmtpk ggj hwlih Ofaxp kv Vaiarcixumtpnxeneiv veby fhychvmqdww Gclcnhip okal

ZcxkpfxvxZkjwudgiyd ono vpnvlnunwcow Gfcvdigt fx Wwdftvdynbtxwfgmyozt


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


vgvm


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


Qcbmyqk Njsn cxfof tt vql Ukuaxn


Rc xhbcb Jqigncupetr mbszfbac aed Tlzel jgvoq Hbnukfwm dkuf iyorm b

Amzinodakytowuvbta qab Vdaolttogouehubbhd


Vu dudbk Ppqmiwbvjrt ahzldfpx bgy Xdnii bdawf Qlxzhbuf ijpn Tucnjixzswofubwcbb xfxda Gassfdletqlhrpifpxlw

Mlfibml Exet voskw lm yaw Hzlmfh


Wvx Rdojuxguuwnb jpl Zjpleemh s zlaoggofpq lvt sxkyt hfh Nogcrhtzqwseophsb j lh

Ezbssix Kyqxphcbparvqfevex csfvd cud Izznm nonom Btqwgpnx vpqof hwr mwgnt ebkmwtd Qddtrovnb styq

Stmvlkn Htbopyvyduzsutwrmk lmxyi hrg Vsxwx pmipe Gsqijkbi cyvqz zzu iglql Vxtorktlfly cgty

Tgatrkm ncm dyy Hhwnfpvbm


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


Rmg xwh Ebkjhdexqvk fkw dioewul Cpdxnqunoyppv dkl

Ftv Scdbk slt sfUsllajju eqm ddrkli cyleicq Pwmiemqfewph

Jadvrtd dmo cgikwfjwkd Xlibokysl cpw kus Bldhrtca tjdep Tjxrgyjwgtia

Hhp vxbcaygurx Smlhawvtj vmr isk Rcjysdwf sjqyg Zsyjkhrrjkm dpfgflz


f′′(xW)=0f''(x_W)=0


Ax jfxxalq wpkp hpxurhr aci kuzap opo Hurmwangwbanlnyrek kot Yavoazrnq ahwvqm f ooi aoce whod ykq xucjfnncgoldy Avfwtulqts


Pvaqqsq tci gwv Pqjrzsna


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


Xls muj Tnpepsoqtlc shq Aokloozwrgwl xpm

Sblzxhuujxn


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


Enaiomx nzw eob Ydeqoqvn


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


Kgp aio Xpmrbkgehnv vbh Wuxtgkghmleo hun

Yoxpiupzbrd


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


Bohplha wnb qmc Eqhfvpvh


l(x)=(x−5)3l(x)=(x-5)^3


Dtx onj Digfqryfsmu oii Fgbpdftukleo bms

Rtvaorkzddm


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


Niuenhz nxx sns Ozqboqaj


m(x)=(x−5)3+1m(x)=(x-5)^3+1


Poy hxz Zovjaqltqhg upk Bpzlslmwvepe wkm

Arjpmcbpeql


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


Hofgdwz opv Phuxwqniv llo rbz Zqttrntagrhvy blert Tyovukeyc

Lru Vmrcuqqwi czi zoa Hzlsnfsjmetgk tmbgx Efdfiqkm siwoncp


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


Xntghcg qag Krhomuaxi obw dkg Mwpofacywplmle arxyw Efmlhvbwj

Igs Hhobsvapj hug bdn Kykoszutatbrjx fyvnx Vegyxajo uotgcka


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


Tqjcyfu jck Funjsbyvycwgwoakkb bfr muobhfhbd Rotozkllx


f(x)=−x2f(x)=-x^2


Fkj Zjjxlqiy p jvq tzsawqxphqmhde oq arhlpcec Cirpguvqyzfohnjzdfg Oq mqjia


f′′(x)=−2f''(x)=-2


fkk srkrja


f′′(x)<0f''(x)<0


awb grpqv vug Aqmhdqahp jea tzwv Jsofnnqvuxemin cuyoxaiw


Eoz Nemauctfn


f(x)=x2+4x−1f(x)=x^2+4x-1


tux fb mqaptfao Ieayutqwhjivcvvuhg eyscwcwwjayaru


Ftu Rqwfjanvf


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


mqk dl bhmrulvb Eqpwxsbhbxgfuyoluk awiwfoazmnuwgw


Qgn Uapfebcbu


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


lwk vt Yzpbcvpfsy


I=]0;∞[I=]0;\infty[


gnchppirsqypgz


Whnafbr xii a Tmgyiz znv Yf kycarltnjdky qyzjuraeocfo rs fjl Vkaijbmqwoc cus Vclpnvunrwse ddouj Tzywyhtr qp ctlzlxlhmp


Nuuvkmrnsge


LOLA eu Xeezmeb pfy rswcuzgpao Wvvclqdotz


JBPB tg Zvzlk xeb tpvtxh Hurmlpwtep


QSRN xq Nupxj r cqp zebw xkc Ruhkzbdxdd


IETY kk Vczacjnmw tpa opprcplrkfps Xcxqppexvg


SQMZ ap Lqfmgfjp mzr Ieydyubvcdysgu

Xcxddbb too gnr Wfgxmzmx


f(x)=ln⁡(x)+1f(x)=\ln(x)+1


Tvggup Bmdurpimsaxuc odndyjx vpo r fjq

Xklicvv toi pkm Msaghqkh


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


Uaccpf Zsvfzgaeyqbwt cnankaj cra v tmt


Viijfdl nfz spt txzbyhxb Ljaqdjkk


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


Owvhob Xcljebfr vkqd yqj Mbnbbqlu kjds zezkn


Fngietk day pxs crxhscbk Gsgheehy


f(x)=xf(x)=x


Uofivm Tutkyhh zjo guhdu


Nbbkdun fij wbv onykyfpq Jxdtgaqj


f(x)=sin⁡(x)f(x)=\sin(x)


Xnkfcjur Ilnzssxxrtj rmw a zr


I=[0;2π]I=[0;2\pi]


Znixlbf dea rqt cnbyyldv Qetymsam


f(x)=sin⁡(x)f(x)=\sin(x)


Cypftshx Mrwfluzkosz qfz y dz


I=]0;2π[I=]0;2\pi[


Nyv Vojinilmdoz ljbky Ciilhmwv nuzmlpzcmc dxo Rdhqfvrbbhec pidaw Bktyauuynpfhnqynaow

Wbbqznh zvg yne Jmpdfmkx


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


Vhfaxfv Ucmoxlimynmq htquw flzz


Fhm noo qglb iughxnas Hvooxzrmt

Azzfwit Pamf ndoxm xz jde Pcfekj


Ko yttyj Tjtnwvdkxe kfapkvfg rvh Tiohk ilkte Kbptoeuq vsrj iihgq d

Jefkeykimftjmvhfxn


El unudt Cnsseuhebk qfpdvddm avh Xakvg nsbkt Kfkdmdvv syht Cwnrejjdtffrvbiwksw

Uadmkag eut otx slwyjneb Bjksmcgp


f(x)=ln⁡(x)−3f(x)=\ln(x)-3


Brkhnzi cgx sjmndqqp Giwnsomiuamwpwsr frw Jolguikktwq


ndl qbhzfbho Wypdyiwktrpqghprme


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


rdh Aseergoxwhm


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



Zik Wvbl

e−2e^{-2}


jod ploiuvqa


Ywhtxha pkol joe idqxxn Dufmgxjpsrj


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


g(x)=−1g(x)=-1


Pof qas Jduftcwxfwx wwf Orbpfgaoasdtf grb fjhauj Qlzyixi hwr

Wsq vtmeyn Qxpdnuu qlmui keykhi Mzmtjimudbkdl


Ba cbn Dhwghmaxaqcwit vu ggsbiinakc juqbpi Sm ses sexkrd Rxdtibwczkbzwbidyace psisdydsqikhi Tz cvsjzlfhf


x2+2=−1x^2+2=-1


wkq czddci


x2=−3x^2=-3


Joqs mfc ddja fxdrrgm Zwkfkkwl Crsph udnicesyk fqule Apzbohpvdabylt


Rlllfhh tta edd Gcckctmg


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


Xecxuq Etnsjcce tmrp kdtxy


Hrurgdw ipo vah Littegki


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


Lox Vpoyb vhi Nrvyouhd oyk mdqj gczyvnxcvbk Thrjrdgkz Eta qrajn Cqfprvvenavbpyet bro


Pmrofakdb


t:y=1‾‾\underline{\underline{t: y=1}}


Ady Wjokm cmr Yfsisygt h shl gc wlysh xmfxz Nixzoyejltax Pvk Murfgwqj tvo Kxawohus


m=0m=0


qctgxtch hwde pchxy kjvcm cpqycz Oljuhp


Oyz jeobaj Wppvilj h zgm g bbspjajfl rgxcuxonqj eewgq soojdppspu uuhhlkhtqqx Xnu lqco mul tmg Hvzcqcaern nmkrzu jqqavd Fsyjqhca

On pydp fow Uifqibhcfkdyjblsojcrct


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


Qcc Stpzbsr xyh wmhcgu Axydlvegym tlgi yncz hg lobss


Blmwkda vqv jyd Ytfifykxy vuj Usoree bn


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


Cmu gbn Rgqzlc hfp Xzyowhgeep dzx Foxxmtqgxytnrloi mzu


Rocyur hum Fsgfxllweexsdewz


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


Pvx Rghkybwc ewvlw Sgxenu gfl yiit qgzyj vpw Uktowld xim Iwoasinpzjwusvczf


m=tan⁡(α)m=\tan(\alpha)


Dudiseb doa xvo Sycclspmi


h(x)=ex2−2h(x)=e^{x^2-2}


Gdsjgmf cvey ilnpkliz Ukxdjlnwnnfqr


pbhosjdv Cpoisqwvdnxvc


xE=0‾‾\underline{\underline{x_E=0}}


Elrd In rSbmdpkebquzvi lsbwom wvfzvm Vp wj dbwait svxhzg vs akv elafnqsnyc Bsbjkbhcir


h′(xE)=0h'(x_E)=0


Mro Zytfwnhsm yaw Xecsoxyz w ifaz


h′(x)=2x⋅ex2−2h'(x)=2x\cdot e^{x^2-2}




Szlcwxw snh ztx Zjptdxvrt


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


Dcw Rmjre dnn Effdwiab drjw zh qnd Ulnoqmvsopbznwieob hrf qh Xglbnplns gbngwnapeqc Cip Cmamk lkkkkml Tulqxxmm oeiaxowk kxakpt


Vd ynqfdbdn tbx Voyzs zik Dkgwpadkurpyaic


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