Mean Value Theorem - 5.7 HEHN VBLUE WEDRED THE MST TOPIC...

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Unformatted text preview: 5.7 HEHN VBLUE WEDRED THE MST TOPIC wE' NEED 70 Comm IS A 77150250 TIMT $1973 sonEr/ums Fanny "oskus mun any SEE” e um: TECHNICAL, BUT H»: cousséusmss 77/197 1935 ewe/19L Fol? 6677mm sman m cm. cows 12' NEXT TERI). HERE‘S 3 PICTURE OF IT : y: Pu) new vmus THEME” : surpass Pm :5 comnmuous on) [M J mvo omssnswnams a» (4,1,). mm 771525 exms A c w («5) 81 wmcu THE 1791065107 LINE IS PBIPBLLEL To 7716 55mm LIIvE Jouwmc rnE POINTS (A,P¢m ) am: (,5, Pm), .1. 5., 01 wmcu Pcb) - plan I FCC) ' b-K 1' wom'r PROVE Tms, euT T716126 HIRE fl NunBER OF THINGS we swam NoncE floor I)“, l. THERE COULD BE new sue» cs . I a. “ conmmvous 01v limb] :s Necessmey, 5.6., 3 . '4. IF Pm) = Feb), man: we THEOPEU says 11m THERE exasrs n c 1» (4,5) :97 wifch Pic) =0. THIS SPECIQL CASE OF THE DEAN VBLDE THEORED IS CBLLED RoLLE '5 TWEOPEU . wE’LL VERIFy THE HYPoTHES‘ES HND Concwslolo OF THE nemu VALUE 171501250 m: on»: swans, EXfiflPLE.‘ CONSIDER PM) =- 4»: on [4,5]. Fax) 15 camnmuous was» 50-! ’, 0’ 1.6., «we» x 7, I, m mnwmk, fix) :5 co~n~uovs a» 11-2, 53. I .._L... Fax; = 45:; so Put) as mrpstasumue amen x > 3. m palancuum‘ fix) :5 DIFFERENTMBLE an: (-7.5 ), FLU ~90.) PLS’) - pm.) ET - erl— _L 3 "' 3 ._—_-—-—— '- .- b-a 5-1. me new VALUE weaken 3335213 mm, FDR sane c no (4.6"), P'Lc) = LET'S FIND IT : p’lX) = 24' ,1... - .L .1675? ’ 3 .2 x»: = 3 40(4) 3 ‘7 w = 3' x = if I I3 name MT ‘95 IS w (4.5) so «:6 my TBKE C = T . WW ‘05 053105 "’5 CoNSEaueMES OF THE n69» vows weaken mar com. 86 NEEDBD no CfiLCUI-US .11: : THE DEmvnnUE 0F I9 comsmmr FUNCTION IS 26170. IT IS Lug? Mus, HowEVER’ mm IF 7W5 oemmnve 0F I9 Fumcnaw as ZERO evsnywvsee am :75 Domaqu mew mt: vacnom nusr BE cawsmmr. 7’ 5.6. I L. mem.“amor ,. .W D.AWH.§WHMM.° m m. u. m. HOWEVER ' IF THE DénfiIN 15 HIV INTEPVHL ’ THINGS fiPE DIFFERENT. THEOREn : IF Fax) :5 commouoos on? [4.53 am: ampeeemmme mo («,5) mm IF P270 :0 F08 BvERy X. no (4,5), THEN 9.x} [5 n comsmm vacnom on) limb], nsne's wHY : LET x as raw Pmmw («.53. men: P as co~n~vov5 on [ant 3 AND DIFFEPENTIfiBLE 010 m,“ 50 mg 05,,” mm; mm“ SAYS WT. F03 5005 c in: (41,30 Fax) -pm) ——————'_' x-a. 2. pic.) BUT He):- 0 so Pun-pea) =0 1.5. ’ Fat) a pan). :r's Comsm~7 .’ [3 TBKES THE 50115 VHLUE BT EVERY X WT IT Wires AT A . THEORED : IF Pm) mvo gm ARE connmuavs on) [0..le , OIFFERENTIHBLE on) cad») mo P'cx) = 32x) pm EVERY x 1N ml»)> TITEN 300 = Pu) + C FDR $005 CONSTBNT C , rm; IS easy 12> SEE : gnu-Pun as coronmuovs on LaJJ’ DIFFERENTIBBLE 0N Ugh) nova (an!) - Fun) I: 32):) - Pix) = 0 0M («,1»). BY anLfiST 1775mm, gnu-put) = C. aux) = Pox) +c FOR $005 CDNSMNT C . EXfiflPLE : PM) = fincsuv x n~o gun): fifikccos X 1935 comnrwws on (—1,;3 ’ DIFFERENTIABLE on (-3, I) mun .I’ I I ch) = fir?" = 90:) an L4,”. THUS, .. mucus x : ancsm x +6 F02 5006 C. PLUG M) X = 0 TD GET - If a +6. ‘L so - BRccas x = Bflcsaw x - 3,15 , 1.6., finccos x + fincsmx *4 If . ...
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This note was uploaded on 10/23/2011 for the course MATHEMATIC 221 taught by Professor Staff during the Fall '09 term at East West University, Chicago.

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Mean Value Theorem - 5.7 HEHN VBLUE WEDRED THE MST TOPIC...

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