Curve Sketching. Calculus U Y2]0x1[5e OK`uJtAaR OSVoufRtIwnaRrre] ]LMLLCr.^ J TAulJlu BrXitgqhItTsq LrfeJsdeKrnv\eydE. Name ID: 1
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1 Calculus U Y]01[5e OK`uJtAaR OSVoufRtIwnaRrre] ]LMLLCr.^ J TAulJlu BrXitgqhItTsq LrfeJsdeKrnv\edE. Curve Sketching Name ID: 1 Date Period For each problem, find the: and intercepts, asmptotes, -coordinates of the critical points, open intervals where the function is increasing and decreasing, -coordinates of the inflection points, open intervals where the function is concave up and concave down, and relative minima and maima. Using this information, sketch the graph of the function. 1 f ( = f( f ( = - f( [ Y0n1]5P ^KEuTtBal HSsoXftIwFafrsei oljlccw.k C gaklzlp [roiagwhftwsa RrReasLeMrfvCeXdo._ XMea\dfe\ awuiptlhq vinqfdienbiutneg BCVamlccGubllubsb. -1- Worksheet b Kuta Software LLC
2 = = f ( = - + f( Y ^m0k1t5i ZKou_tOa MSUonfgtrwmaVrkeI elclecu.y a BAellE jriog^hmt[sm WrpeXs[eVrivKePdQ.n e vmyakdkeo `wpihteht KINnUfwiRn_iAtfeR ncialncuhlzupsi. -- Worksheet b Kuta Software LLC
3 f ( = f( f ( = f( = V _O0J1q5o CK_uXtFak JS_o\fWtTwKa\rbei MLiL]CN.k V ]AOlFlp nroisguhvtvsl ireekste_rzvoemdm.] k _MuaRdTeg `wsiqtshw EIrnBfFimnwigtNee ACuaglpcAu]lUuis]. -- Worksheet b Kuta Software LLC
4 9 = f ( = f( f ( = - f( K Vr0]1G5 VKFuVtNad osgoqfqtzwuaryev YLSLKCl.K R wa]lnlk MriwgGhVtMsf JrbefslewrUvDedE.B Z cmpavdaek Vw^iJt]hV zifntfaimn`i\tue\ ocyafluc_uylbupsl. -- Worksheet b Kuta Software LLC
5 1 = f ( = f( a Zt0O1H5B pktuktra\ oseoofwtswganrleh `LtLHCh.f G OAIlPlA FrvigihltMss Yr]efsbeqrFvAegdg.I p OMaPdZeE OwsibtMhA `In]fbiFnHiqtne ]C\aoliciuDlFuSsF. -5- Worksheet b Kuta Software LLC
6 1 = = = u Qn0t1\5] vkhuxtyaf jsvoyfptgwaa\raen mlrlwck.q e IAlnlC GrRizghPtasf QrAensDeBrCvdeMdF.H o RMnaKdbeD bwbiutlha NIjnJfmidnjintSeQ YC`a[lYcruuliuKsR. -- Worksheet b Kuta Software LLC
7 17 = = f ( = - f( X [`0H1f5a \Krurt_ak sszowfltdwtarqeu ]LCLtCR.g n LAjlElT erki_g`hdtcsb HrOeJsBelr]vaeDdD.H q SMAaudKeb BwiietOhf OIfnwfBianBiZtBet ZCawlWcDuNl\uqsM. -7- Worksheet b Kuta Software LLC
8 0 = = = V km0o1m5z KAumtNaw DSVoJfgtrwMaurheC olrlice.s b UA]lvlf Or[iPgdhat]sQ ^rjecseewrsvleqdd.] X smraidsez WwDijtUhp GIonSfmiVnniXtGeE ICGazllccurlWuDsO. -- Worksheet b Kuta Software LLC
9 f ( = - f( = f ( = - - f( V gk0t1i5n lk`ultan ssxoafjthw[ahrmej eluloc`.w Z sa_ldli rr^ioghhat_s` zrkexsvewrcvheqdv.a S HM_aDdbeG fwliqtvh] rivnrfqignsiktdek ocuailwcwutlcumss. -9- Worksheet b Kuta Software LLC
10 Calculus ^ nz0h1]5r TKRuLtoaM osho[fktjwwatrjek FLELaCn.D S vaoldl` brqiwgdhdtysz Urreps[evrmvfeFd`. Curve Sketching Name ID: 1 Date Period For each problem, find the: and intercepts, asmptotes, -coordinates of the critical points, open intervals where the function is increasing and decreasing, -coordinates of the inflection points, open intervals where the function is concave up and concave down, and relative minima and maima. Using this information, sketch the graph of the function. 1 f ( = f( -intercepts at = -, -intercept at = No vertical asmptotes eist. No horizontal asmptotes eist. Critical points at: = -, 0, Increasing: (-, 0, (, Decreasing: (-, -, (0, Inflection points at: = - Concave up: ( -, -, (, (, Concave down: -, Relative minima: (-, 0, (, 0 Relative maimum: (0, 1 f ( = - f( No -intercepts. -intercept at = - Vertical asmptote at: = Horizontal asmptote at: f = 0 No critical points eist. Increasing: No intervals eist. Decreasing: (-,, (, No inflection points eist. Concave up: (, Concave down: (-, No relative minima. No relative maima. Dp0R1q5_ tkeuttoay \SVo^fztDwzaNreeH lltlect.t t gaglblp crxikgzhetasc UrAeCsAemrBv]eIdW.b N IMVajdXeF bwoivtkhj nitnyfji\nbiit_ew ZCnallFcvuJlYujsK. -1- Worksheet b Kuta Software LLC
11 = = intercepts at = - 1, 1 -intercept at = 1 No vertical asmptotes eist. No horizontal asmptotes eist. Critical points at: = - 1, 0, 1 Increasing: (- 1, 0, (1, Decreasing: (-, - 1, (0, 1 Inflection points at: = -, ( Concave up: -, - (, (, Concave down: -, Relative minima: (- 1, 0, (1, 0 Relative maimum: ( 0, 1 No -intercepts. -intercept at = f ( = No vertical asmptotes eist. No horizontal asmptotes eist. Critical point at: = - 1 Increasing: (-, - 1 Decreasing: (- 1, No inflection points eist. Concave up: No intervals eist. Concave down: (-, No relative minima. Relative maimum: (- 1, - f( -intercept at = 0 -intercept at = Vertical asmptote at: = - Horizontal asmptote at: f = - 1 No critical points eist. Increasing: No intervals eist. Decreasing: (-, -, (-, No inflection points eist. Concave up: (-, Concave down: (-, - No relative minima. No relative maima. X sd0w1n5i hkwuetia_ ISOosfRtgwTaArbeE tl]lwcv.o Q AtlQlN RrbiOgvhYt^sC prtecsxetrhveewdf.m ] NMtadd\eN nwtidtbha ^ITnDfmiNnRiStaeZ JCAavljcguelMumsc. -- Worksheet b Kuta Software LLC
12 f ( = f( f ( = intercepts at = 1 -, 1 + -intercept at = No vertical asmptotes eist. No horizontal asmptotes eist. Critical point at: = 1 Increasing: (-, 1 Decreasing: (1, No inflection points eist. Concave up: No intervals eist. Concave down: (-, No relative minima. Relative maimum: (1, f( -intercepts at = No vertical asmptotes eist. No horizontal asmptotes eist. Critical points at: = - 5, 1, 0, intercept at = = Increasing: ( - 5, 1 Decreasing: ( -, - 5, (1, Inflection point at: = - 1 Concave up: ( -, - 1 ( Concave down: - 1, Relative minimum: ( - 5, ( Relative maimum: 1, 1 -intercepts at = - -, - + -intercept at = No vertical asmptotes eist. No horizontal asmptotes eist. Critical point at: = - Increasing: (-, Decreasing: (-, - No inflection points eist. Concave up: (-, Concave down: No intervals eist. Relative minimum: (-, - 1 No relative maima. o Ma0n1A5v rk\uhtfaf JSIonfptaw[a\rhee GL]LUCw.I m oadl_li prlilgnhhtcsz [rxebsfegruv[emda.q b smwajddee owkietbhe wimnf_ijnwiitmej CCaSlHcguhl^uWsc. -- Worksheet b Kuta Software LLC
13 9 = - + -intercepts at = 0, -intercept at = f ( = No vertical asmptotes eist. No horizontal asmptotes eist. Critical points at: = 0, Increasing: (0, Decreasing: (-, 0, (, Inflection point at: = 1 Concave up: (-, 1 Concave down: (1, Relative minimum: (0, 0 Relative maimum: (, f( f ( = intercepts at = - -, - + -intercept at = - No vertical asmptotes eist. No horizontal asmptotes eist. Critical point at: = - Increasing: (-, - Decreasing: (-, No inflection points eist. Concave up: No intervals eist. Concave down: (-, No relative minima. Relative maimum: (-, f( -intercept at = 0 -intercept at = Vertical asmptote at: = 1 No horizontal asmptotes eist. Slant asmptote: = + 1 Critical points at: = 0, Increasing: (-, 0, (, Decreasing: (0, 1, (1, No inflection points eist. Concave up: (1, Concave down: (-, 1 Relative minimum: (, Relative maimum: (0, 0 R AH0t1j5\ hk^u`tvah [SLoWf`tSwPa_rew _LbLeCW.P f lafl\lm [rmiagyhvtrs\ erkegsweoryvieldi.] c SMmaDd[eP ewqijtphd hipnefti_ntiythem TCfablHcduZljunsv. -- Worksheet b Kuta Software LLC
14 1 = - 5 -intercepts at = - 5, 0, 5 -intercept at = f ( = No vertical asmptotes eist. No horizontal asmptotes eist. 10 Critical points at: = -, 0, ( 0 Increasing: - 10 (,, 10 Inflection points at: = - 0, 10, Decreasing: ( -, - 10, ( 0, 10 ( Concave up: -, - 0 (, 0 (, Concave down: - 0, Relative minima: ( - 10 f( -intercepts at = No vertical asmptotes eist. No horizontal asmptotes eist. Critical points at: = -, 0, - 5 ( 1, 10, - 5 1, 0, 1 + Increasing: ( -, -, (, Decreasing: ( -, 0 Relative maimum: (0, 0 -intercept at = 0 Inflection point at: = 1 Concave up: ( 1, Concave down: ( -, 1 Relative minimum: (, - 1 Relative maimum: ( -, 1 k lt0_1_5r FKjuvtdaR usbocfktlwha^roeq RLzLsCu.i E kadlplx srciwg^hftksp ^rbeis^egrqvyeodf.n d PMcaqdweq AwDirtPhg ZIpnFfvianairtdeq rcgapldckuglruase. -5- Worksheet b Kuta Software LLC
15 1 = = intercepts at = -, -intercept at = 1 No vertical asmptotes eist. No horizontal asmptotes eist. Critical points at: = -, 0, Increasing: (-, 0, (, Decreasing: (-, -, (0, Inflection points at: = -, Concave up: ( -, -, (, Concave down: ( -, Relative minima: (-, 0, (, 0 Relative maimum: ( 0, 1 -intercepts at = 0, -intercept at = = No vertical asmptotes eist. No horizontal asmptotes eist. Critical points at: = 0, Increasing: (-, 0, (, Decreasing: (0, Inflection point at: = 1 Concave up: (1, Concave down: (-, 1 Relative minimum: (, - 1 Relative maimum: (0, 0 -intercepts at = No vertical asmptotes eist. No horizontal asmptotes eist., 0, intercept at = Critical points at: = - 1, 1 Increasing: ( - 1, 1 Decreasing: (-, - 1, ( 1, Inflection point at: = - 1 Concave up: ( -, - 1 Concave down: ( - 1, Relative minimum: (- 1, - 1 Relative maimum: ( 1, 5 7 h Ai0Q1M5h XK[ujtnaW BStotfztwwLarrdeg sljlc.e r VARlnlH vrdieguhhtosg trce\snemrmveidg.[ ` RMEa\dMeM KwmiDtchs `IGnkfUi\ndiMtet hc]aglpcdullnuss. -- Worksheet b Kuta Software LLC
16 17 = = intercepts at = - 1, 1 -intercept at = - 1 No vertical asmptotes eist. No horizontal asmptotes eist. Critical points at: = - 1, 0, 1 Increasing: (-, - 1, (0, 1 Decreasing: (- 1, 0, (1, Inflection points at: = -, ( Concave up: -, ( Concave down: -, - (, Relative minimum: ( 0, - 1 Relative maima: (- 1, 0, (1, 0 -intercepts at = -, 0, -intercept at = f ( = - No vertical asmptotes eist. No horizontal asmptotes eist. Critical points at: = - 1, 0, 1 Increasing: (-, - 1, (0, 1 Decreasing: (- 1, 0, (1, Inflection points at: = -, ( Concave up: -, ( Concave down: -, - (, Relative minimum: (0, 0 Relative maima: ( - 1, 1 (, 1, 1 f( -intercepts at = -, -intercept at = No vertical asmptotes eist. No horizontal asmptotes eist. Critical point at: = 0 Increasing: (0, Decreasing: (-, 0 No inflection points eist. Concave up: (-, Concave down: No intervals eist. Relative minimum: (0, - No relative maima.,, i gg01o5w TKhuct_ak usqoyfotpwdaqrreb ]LOLGCV.V N ia`lvlg TrdiQgnhatfsZ LrSeJsseErgvTeidv.T [ M`a`dUeE MwkiotKhE HIVnQf\iKnji`tbeg QChazlLc^usl_ubsX. -7- Worksheet b Kuta Software LLC
17 0 = - + -intercepts at = -, -intercept at = = No vertical asmptotes eist. No horizontal asmptotes eist. Critical point at: = 0 Increasing: (-, 0 Decreasing: (0, No inflection points eist. Concave up: No intervals eist. Concave down: (-, No relative minima. Relative maimum: (0, -intercept at = 0 -intercept at = = Vertical asmptote at: = Horizontal asmptote at: = - No critical points eist. Increasing: (-,, (, No inflection points eist. Decreasing: No intervals eist. Concave up: (-, Concave down: (, No relative minima. No relative maima. -intercept at = 0 -intercept at = Vertical asmptote at: = - 1 Horizontal asmptote at: = No critical points eist. Increasing: (-, - 1, (- 1, No inflection points eist. Decreasing: No intervals eist. Concave up: (-, - 1 Concave down: (- 1, No relative minima. No relative maima. z QX01h5n lkvuftfay JSloOfTtKwfaqr`eU NLELbCa.S r `ANl]l` vruisglhutqs] [rgetskeqrlvjeadx.r m wmlamdreg Mwni]tthl piunaffion^iytbeb icfal]cvubl\uusp. -- Worksheet b Kuta Software LLC
18 f ( = - f( -intercepts at = -, -intercept at = = No vertical asmptotes eist. No horizontal asmptotes eist. Critical point at: = 0 Increasing: (0, Decreasing: (-, 0 No inflection points eist. Concave up: (-, Concave down: No intervals eist. Relative minimum: (0, - No relative maima f ( = intercepts at = - 1, 1 -intercept at = - 1 No vertical asmptotes eist. No horizontal asmptotes eist. Critical points at: = - 1, 0, 1 - Increasing: (-, - 1, (0, 1 Decreasing: (- 1, 0, (1, Inflection points at: = -, ( Concave up: -, ( Concave down: -, - (, Relative minimum: ( 0, - 1 Relative maima: (- 1, 0, (1, 0 f( -intercept at = 0 -intercept at = Vertical asmptote at: = No horizontal asmptotes eist. Slant asmptote: = - - Critical points at: = 0, Increasing: (0,, (, Decreasing: (-, 0, (, No inflection points eist. Concave up: (-, Concave down: (, Relative minimum: (0, 0 Relative maimum: (,, t X0D1g5F lkgubtsaw JSPoAfGthwEaOr\eU ZLKLmCt.[ e ZAilBl` zrdiogyhdtfsl Ir`ersoemrDvoed\.V g AMmaqddeJ lwtivtrhc OI_njfcionuiJtAeJ JCkaellcVuNl^u]sq. -9- Worksheet b Kuta Software LLC
Math RE - Calculus I Application of the derivative (1) Curve Sketching Page 1 of 9
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