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Slope = Average Rate of Change between P & Q0p  282-2 p 3fff___PPT10i.y]+D=' = @B +"  ,m(  , , TW?Rectangle 2]] 2   , TW?Rectangle 3}  z  ] C   , fA??allPicture 4allz 3fff___PPT10i.n(D +D=' = @B +"wT jb0J(      x`W0e0e?Rectangle 2"ûPK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!ݕSVtdrs/shapexml.xmlWO0 ]"ۤ Ui8mVl0Mc/LD"w-'b|cts&uiF/3|=g>] e;Uv2r%[+5dq`r`RUѠSқ.QfXS!wGCδhRb$A17? r>i!4SJ1bwjJ 7Q&(6x4>:I~%t&lLu3= @wٵHCpF6Dw̨%f xV֊0׹-ljU8ˈBr.LVF@׍l(p?ZFPVyH A+4z$Zb"VD!K1gn1R!HL Ȯi&3.ޗ+ݡ֔k֘BmHqC ЈZԝ8ҴTs+?EV m([8cH6̔49oJNQME6ڃjmZk5@BWLW5+T.EwQFΪ&g`؆ǩ,WPq[;`g;N\(mZ-J`Y) H?RÔ}O1{dZM c.^l2nϻ?Y/stNPK!)sdrs/downrev.xmlDMO0 @HM TM ו!^~&)Ihֳvb[3JoZW+8nAĄ`)Pfvi(R-Xb \X6d1}OYc 8vre+iu| ŷUFC ZhnDS_Ί*W /W ZsĘ((>e rPK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!ݕSVt*drs/shapexml.xmlPK-!)sdrs/downrev.xmlPK `}   Tangent Line to f (x)H EEEEE     xX0e0e?Rectangle 3"f`PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!:Ԕdrs/shapexml.xmlXMo6 x-FE m#0,PeH;oHq^~ 7h_}Vmu }r&ufR/3΅2Z&|':zjMꄯ'V\al%[݉T$(dJX'~? c$ '\1/Ҙbb?mmTV$>@纩UFۄK}mK8K#$\XS0Ygki43R]kEjG5mW[%E؇p*MOmJqU4/aXODZ, zĄKX,U}9R$-I$Qv`*WA.^7Tz~sl3ӏ۠džGV3#R"NdDmO xSe8ԎW+=2TN|MMyO?tOORWݥWSOjǷϤx7~͂xC\tPK!( drs/downrev.xmlDJ@Ea7ЦݖЦ0fI4v6{q8ùz08 n' ӭǛ9j%#X./kw;:c-XbC \P5d0L\OyO_Krɻ$I{*FAm^7yY.֟_6 泱WeRǧ÷z!W}\PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!:Ԕ*drs/shapexml.xmlPK-!( Odrs/downrev.xmlPKU  0The line through P = (a, f(a)) with a slope of,Z  77777 1 0  rA ? ?Object 4S"11 13(   3fff___PPT10e.+D=' = @B +"  T   @ (      xX0e0e?Rectangle 2" PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!'Z[#ddrs/shapexml.xmlWQO8~?  *qwR*8mZªEg%Y c+RzOP\Zɐ*Jt+,6flʎ.kƽKQ3U7BAWjS3Y#P98e//z5Uj5s%~R)MaBb5 R:x!+O0aO §.M\oo/B>fIܶArRPDI  F;}6$ƛ?䊍uYNEDnSzr!#v6G8h03D^$Ckns?/eԚE0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!ۛQ6drs/shapexml.xmlTn6?Y^ I5E$>ZǛCQ@5CΛ8sIvֵZ|3*]j/W79O&I8y/&sr{FډmѶ#ݎN(O:9\_F/q:fcU=65̧cQ!퓨b+puw?`jK/;L-J#^MY_vj>#(Ujbv̟ PKd1]ŧ` oźX4ev? yKnR^N9ς䔉g7bu%dxS8]$c4}vdASx:47쥧[i%#U֜Wr6+=ԬtgȯUa/ʁG]Ȉ@AظMDK?I$)QoƲPGvsp)U50$U-g*ׁ{YսG]6[o޻G-Hlge7h1SԦ lQ7 sޠ&$/KKnsʇ#Yߥj;>8lo+Frۤ_Ͽ(+j B,PK!ȶdrs/downrev.xmlDN0 HCIXZe6zVk{{,p_/V@1(U 7OΔ`X`a4V"@ s_hy ;eGNdٝvz`OO Uݷ3yQ~bXeRs5֏&aUVz>n11EBA/PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!ۛQ6*drs/shapexml.xmlPK-!ȶdrs/downrev.xmlPK0 `   Q Derivatives  E     x X0e0e?Rectangle 3"RLPK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!L$drs/shapexml.xmlXn6?~ď؈|H[0\e@I"Yr|}Iq.Bc9sX]-Ȗ[)ޗ.%\f*:.(ɜ %yBүS K; -Nf%4+Ԭ;p˥cjwN*IgJnWzi(]R2zHV=b-8.aPƶ`?_ Rj%cSYn2vV .kLU]πDA.d0a{C<^!z6hk6UEAz<͔raؔɰ}5  E;2 FdzvΟA"E1gsIgJ φN]Io04&ḏ9IOwdSϕc2í uaTfn!W:>m{`F?!pMJy0`ۅuP_"[=AJBn5nbCXO"P0fKXdjL5@ %9/XC<.l!o&\(n¡Y6lqJl n"sZ-3Ģ?N-nyr>½=\ v7m MqL"RTr8ڤq (Uq^jk7=b!SJJ\JT_]̩/ }㏨q*'ܳ a畯{\Yǜw{d&xwWn|؅le'87Wǯ"swW??ճPK!|FXdrs/downrev.xmlDN0HHܨRU) "Uj%&x٦MWO3 r % +[ʗ15vI<̦g̵=EEQABK髆 #[g0R;0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!-drs/shapexml.xmlVQO8~_ a[Ba8mJӉԀRgl|8W_ֵ +MdBO?)2WE% xw2X& & pC\骉MCXI&L53U%t5hnZ~WJkl%Wi3n߯TEB`Q"Ycx'悓:ʗsg ͞?Thr3xiYa4y_|p,4VVp D2w 5vx Y.u__X%Q4MBO΀"|mI|4 AlE/x 5]ߪbVg5򏣌\HgJ4毖i&J<: 2w5ٮFX O9vMhn5%A[3WuDMdM}\g!nνJހ&:wmpcSAR"(j0>,0T3=I(` aJ=V/Y>w;ml"ocX*io*Yvj,q2cw^&斬c_p▗m_̰U{SY;qy;C[-͛XY 4#7 .ۺՏ*ɷ-蝻H6G%TQ>w%YĔtmSTO/:E嚯MR`̚ڎg~G籐-]%D%%Mz])c׾"XD:nj-x"h+z6+.$g#vo_dom'uwc,:?NZ{,(rN|ȶdF+{D2='$1\r\Bf~p̂Ĉ=?(;7D3%vCψ77_ p߇i>_淲ws{IcOOUN0 (W4m !PEv`ar[w&U¶'IK!q-yϱ8Eg䖹c%@!1+,eaZ0@47N >@mG5z]sfON&uiWZ{Pu8ۣQ1LuURT@OqE/^hҸcl# _=]XM`m d0*1²-$qheԘg(.u&F靯G6~cxLj6YrG ?H,!ׄw6LMrg%O/F ڰ,MY>2B_:qG]iPK! 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Jdrs/downrev.xmlPK@    zEx 2: Find f (x) and use it to find the equation of the tangent line to f (x) at x = 1. ^ 222222922222 ^ 0 lA ? ?Object 3@ (   3fff___PPT10e.+D=' = @B +" & U\ ) ! p0 (  0  0 C  X0e0e?Rectangle 2" PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!y[Bdrs/shapexml.xmlWO#7^$" VPD8#z=oMN)=͛gryU)֕F'˙ԙK=O۫cΜ:htٯcW3,n\'|}=t\pL-5|yIFQgx^%+^N-+n3-*l{#3$1WyK޵ɈoI&'|w\`7ynyXH;ƾ&WT)zFW'Qdخ y]8 [} NֽQ 9['ׅX<gcD'fBΨ2*z1䥲l)Ty(#vhc0HD{}mpbك(RjT7 Qԓ>覺48"toc2SOhL󷫿 (ȵ-D-CXN'= D9?kwWC UN`C-&J)*6,ŭHg-RL yX GՂ~蝛}:p$B/5l=/ĵ޴oش=+;/X17T7ۙ'ڠ7='ٶ=ձY8#<QNLijU>?V%)M1zڱ/ፔԆ4#$0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!Yc drs/shapexml.xmlUO0~ZB6"ۤ Uiq6cgSZ}C)vEܮEvRPD(&g7ڸ9Yf2߆?`*I2>EЈb||:(,14chmWy(M,QF9HGJ g `_pFftz1Pfe(Sf;CIdfYzYҢIs ]'ƞJ *, 7K Ȯn:3*ѷ+H. .5 B"Al(/ eÆlSV9o(R{t2ϲgi_.?ǴC}[Jݴ~ySM5C)gOD~9V(D/&S_PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!Yc *drs/shapexml.xmlPK-!9qdrs/downrev.xmlPK@    Ex 3: Find the slopes of the tangent lines to the graph at (0, 1) and ("1, 2). $S 2O2 S 0 lA ? ?Object 3  (   3fff___PPT10e.+D=' = @B +" xMOAl, z҈L8桋nC 5*FM&DQ^4c&cֵP57o}̼-AP Bc!rTȹl.)1Wuۈ25~ADw ҅෰Sg.׹R5gkyKCL[#εǗF3)X8+툛7,1 K@m!9cġS|CS~uc}#UHo@􂕯e?Fã(ց~IwFS۸tFZzoSS wz*W}5A\ln z[.4={Qƃi+xEUe&]bM 䥐7S, NY1H;m8hqt Z ݧ4#bF4Q^T~9Euj97zgDwO=Ș#Y95 .E#-Gb\u~+w};+7B칔 8B bL*V鉑YފH.nY?6cjBI jߒkB3_;rra*?Uwľ}v}]E"ؙ\;{U[ȭdf& ,2Y606o$G |\=O_{tN~Cy`lEdrWiw\(7=N2(ܟBbg|F7A@xҵ̿bC+wgYy{*N$lH9: Km~A8oL 3$zj3\WC P`e?baUֽ3'bX(XT)Zy`~N+ _=-/2?(@xWOSA>Z AB8iz$*E9<Ti XzP $^L< Dh<# `3kj-ՐHefw;3ovfq&y'P4d؞'p̾L6.8[ME3D6'{TO,ΜM]*zfߟk`Tec'~02^pMь>>!T9!EE\iZlIZΜ*S·GzS쳿f![ysZM^L` A:a:Q~u֩tQ]v6'mf|9pwz|wWs6弰u \ni1Y[=U&9 m7yCιiQgŎ0c0UEV+8Қ(GZ$T(-̾Z$u45Ae;52`bt 5[ Oìw0tIGZ5sUd }ac  ]PXZ|MjY0t e>\oCZyuiˡJ}'!eK O"X`AqOM`/NA[#?O{}AդTNtW?AI͸+{rÓxl$NLXqSYw קj=b"ߋI (B[ߤY c./A[؏f%)ZUqqȾ0 UUt ʐmxXMLSAע}Xp%'1F1ӆJEؓ 1z#M9xGx$&Mċ֙}hI!73ȟzX0hO 4Ɛpx"! 9F~#WE Ѕ!f-"f}vm٥L/7fyt7qyCFىwL)S La'I2r!a8b=h@f rP4|z/Sߑ}ݡ.vch̸ ׁ<"|]@f~ @]>`>q ZlxS<7=snl ȹ > b y3Wت~ʓW7*"Y,c;c| W**5{ 8U0O9Ar8{S,88VIyMP P;T.P-`d9mSx,e- _UV +Qc\6˚rSl {2FW8ɆhGklrg|Z`-ӗC^K,ا_'k6#f$ͥyJsOPXh;np|Xgu0 P O砀u )GO;:*fS>yp*Մl߾S9@wzXD?FMrM@~׈ ہ|8p_ cǂ $1U U~c7$Net;A1$~?Zc~g`=عd. L·p9DHrLrx#BP_zr~~dzɞIE#xCB+g'jE,2w׿{xz%HG@{ Li^CTecof0L="v;}=^_ve}LpRF߹}Agق|]pٲj,(a.eW%hngSKx,NAGsF^/I}^MyIًnPk}|JdQijo.J(8PɬaBe+ j&G"wkKUt' P?M:}WAr(9z[o(>yn:}0͙%3SVg+Z0 꾁(t' 샟]bj%tb1O U̸q}$8jR$Ltm( OfrY>C@RUHRzUcGU̟Vc&S䏿>Z란ְJ"oDo\VDmh ;ڵ,39Tҧ#q ®M2;bSP=a$3?SHT1޼OWq#xXOQ|tP#pX9H8(ZTR 5ZH9Y<{h<Q͘('֙R" }̼f~k}8XY/T1?@,Mi(2J ?Pc($!s`:Kq @=7X.׹E( !2k,nNbS2{uHag?r8`phO=P>7QrG#.qFOcunt$UWeY0f~ u $@6sۛna%Jٿz~r@5>X Z:y_.׉D3P?_hkDkiQ"Uˋi+JVf4BM==D|(*1w$6*-]C&jkmW^FvoMQ'ks5u>pd:Rی5>,#.>ۯcf|29=ԫo a#_4H;-vEjdZ=&k5N&ڤ{#)#Y0Fp`]&?_E&!:g 2ѳ_s}:ZI&M7?Cs~޲_%ꨩK6q$et$AK4̼K0@cF-Oh+'0 hp    (02.1 Tangents & Velocities jbaldwinOrbitJuliette Baldwin45Microsoft Office PowerPoint@ u@M@0hGg  pp  pA x(x{{{{sskkccZZRRJJBB9911))!!{{sssskkccZZRRJJBB9911))!!{{{{sskkccZZRRJJBB9911))!!!{{sssskkccZZRRJJBB9911))!!{{{{sskkccZZRRJJBB9911))!!!{{sssskkccZZRRJJBB9911))!!!{{{{sskkccZZRRJJBB9911))!!!{{sssskkccZZRRJJBB9911))!!{{{{sskkccZZRRJJBB9911))!!!{{sssskkccZZRRJJBB9911))!!!{{{{sskkccZZRRJJBB9911))!!!c9{{sssskkccZZRRJJBB9911))!!cB{{{{sskkccZZRRJJBB9911))!!))!{{sssskkccZZRRJJBB9911))!!!!!{{{{sskkccZZRRJJBB9911))!!))!{{sssskkccZZRRJJBB9911))!!1!){{{{sskkccZZRRJJBB9911))!!)9{{sssskkccZZRRJJBB9911))!!!!!){{{{sskkccZZRRJJBB9911))!!)19{{sssskkccZZRRJJBB9911))!!B1){{{{sskkccZZRRJJBB9911))!!B)){{sssskkccZZRRJJBB9911))!!1)9{{{sskkccZZRRJJBB9911))!!))B1sssskkccZZRRJJBB9911))!!)11){sskkccZZRRJJBB9911))!!)9)sskkccZZRRJJBB9911))!!)9!)!skkccZZRRJJBB9911))!!)9B!kkccZZRRJJBB9911))!!)9B!kccZZRRJJBB9911))!!11R!ccZZRRJJBB9911))!!B!B)cZZRRJJBB9911))!!BJ1ZZRRJJBB9911))!!B91ZRRJJBB9911))!!9191RRJJBB9911))!!JB)!RJJBB9911))!!91BBJJBB9911))!!1!1BJBB9911))!!9))1BBB9911))!!)!BJ!B9911))!!1)B)B9911))!!!)))1B!911))!kc1!9!1111))!)sZ1)BR11))!!B!!1sR!!!)!!B)!!!!!!!!!!999111BBB999111ﭭccc!!!!!!!!!֭ZZZﭭcccƥ)))J)RsssR!!kJJkƵ111kkJƵRkkƵ111R!)sJJJ!!!JcskƽJJJZBBZRJkssJ֌{΄JR!k{{kƽBBBZBJcRJ{ZZJJJJ!!!JsR{{{R)Jks!kkRcccքJR!kskބJք{{{111޽ƭ!RJ!!!JkƄR111JsƔkkZZZ!!!΄JR!kƔkk{Z{Rk)))J!!!JքJƽJcJkkZZ{޽ε{{J罽ƔkkZZ{ﵽJcJƽJ!!!RJksBJJkR!kkkkkJkZJJR!kkkkkJksBJJJsBBJJ甔ƽkkJJkkkkkJkkRkkkkkkkkJJ{sJsssJksssJJJkJkJk111RRRcccRRRsss111k9Z999BBB!!!999111)))BBBkkk!!!ZZZ{{{{{{sssBBB֥!!!!!!sss޵便ccc!!!!!!111!!!BBB!!!!!!!!!ﭭcccƥ)))スcccƌJkkJJkRkJssJBBBkkքJJRR!!kJJJƵ!!kJkJ΄JJR))sRJk!99s罽J!RތJJJ甔{{{ֽ!!!JBBBJք{քJJJJkƽBBBZBBZRJքJ!!!JJքJJkƽBBBZBBZRJ{ZZJJJJkֽkRΜJJބJBBBkRccc΄JJքJkƄJބR)J΄J!!!JJ΄JJքJބ111ƭ!RJkkkkksJkƄJkƵ111JBBB!!!΄J111JƔkJΔkƄR111JƄJ)))JJ΄J111JƔk{Rk)))Jkƽ{JkBsZZZR!kkkZZƽJBBB޵ε{{JνƵssJss{εƄJƽRkJֽεssJJJ΄JνƵssJƽJcJƽJBBB111kRRR罵kcsccsJBBBJkZJJks)JJkRJJksBJJks)JJ)))JJkJks)JJksBJJJsBBJJZZ{kkkkƵJRνRRRޥRkJkJJkkJkk!!kJJJkkkkJk֥s{{{JJ111cJkBBsJZkRRR{JkJ{{sssk!!R{kkJkkkJJJkJkJkkk՜.+,0    pOn-screen Show (4:3)Deer Valley USD[   Arial WingdingsCalibriTimesSymbolOrbit1_OrbitMicrosoft Equation 3.0!2.1A Tangent Lines & DerivativesTangent Line: a line that intersects a curve at a point P & whose slope approximates the behavior of the curve at or very close to point P. Slope = Instantaneous Rate of Change at P pSecant Line: a line that intersects a curve at two points, P & Q. Slope = Average Rate of Change between P & QSlide 4Tangent Line to f (x)7Ex 1: Find the slope of the tangent line at x = 3 Derivatives`Ex 2: Find f (x) and use it to find the equation of the tangent line to f (x) at x = 1. W 2.1A pg. 103 # 1, 3, 4, # 9 – 33 EOO, # 71, & 77 (use slope limit for 9,71 & 77) UEx 3: Find the slopes of the tangent lines to the graph at (0, 1) and (−1, 2).  Fonts UsedThemeEmbedded OLE Servers Slide Titles (_-Juliette BaldwinJuliette Baldwin  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`bcdefghjklmnopwRoot EntrydO)PicturesCurrent UseriSummaryInformation(PowerPoint Document(-DocumentSummaryInformation8a