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# Calculus 1 MATH 161

GPA 3.58

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This 11 page Class Notes was uploaded by Vernie McCullough on Thursday October 15, 2015. The Class Notes belongs to MATH 161 at Millersville University of Pennsylvania taught by J. Buchanan in Fall. Since its upload, it has received 6 views. For similar materials see /class/223526/math-161-millersville-university-of-pennsylvania in Mathematics (M) at Millersville University of Pennsylvania.

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Date Created: 10/15/15

Comprehensive Graphing 1 Example 1 Suppose we have the following function and its rst and second derivatives 4r fa i 274x3 4 3 7 2 Hrs 2 2 r 7 4r 3 Wm 8amp3 7 9r 12 2 7 4r 33 The graphs of the rst and second derivatives resemble 73975 715 A 710 720 We can estimate from the graph of the rst derivative or solve algebraically from the formula for the rst derivative that f i 0 It is very di icult to see from the graph of the rst derivative that f lt 0 for m lt 73 It is very di icult to see from the graph of the second derivative that f lt 0 for m lt 73522 lf f7 m 705367 m 774647 and f73522 m 70478 sketch the graph of 2 Example 2 Suppose we have the following function and its rst and second derivatives 3 x fa 2 7 2 7 3 7 22 7 4 7 9 f 7 2 7 2 7 32 272 18 27 f 2 7 2 7 33 The graphs of the rst and second derivatives resemble 10 2 5 2 2 4 6 8 4 7 2 4 6 8 V 2 5 75 V 7 5 710 We can estimate from the graph of the rst derivative or solve algebraically from the formula for the rst derivative that f 0 07 f 2 7 07 and f 2 0 The second derviative is equal to zero only at 0 If f0 07 f2 7 m 71484027 and f2 m 10234 sketch the graph of wo s 133 quoty 397 5 1 bu to39d w 1 we to ca M M39W 0 x 01 Mto 1 mix1 10 C 39B A 39b B Wye x 2 n quot I 6 6 5 Ms 12 39 xw WHLw s 3 gigs 11 25 33 mt II M quot 5 MW 2 v125 262 MluoN HQ 9 quotCu u I quotN 4qs w Saw N OBIQ 33 3 Obi6 IHRI AampampN 23x colq d NR mi 13 d 24 2 T423 4Q d 0 Cyanlilllli vi a 2 NQTEV Cw 3w 32f 39 Mhlbl amp 639 23 653 quotLt31L 0 z m 9 ZWQ G2 Xv 23232L3 no Rec 39 90 wk 44Kampzo 39o M 0 90 1 M 7kquot3 kao 0 uM R90 7 7 await W rm 7 39 az 7xz La Io 397 I a W M MAIlpl amp b7 25 v6msz r 1 m M hdq m Rec Z o 3 01 quot10 amp um 514 mg XV T 39 7413 QM39W 2 2494 190 11249 m 4 KQo Rag 39 12 m m quot2 m M quotI quot 3 0 em 2 quotLZGcQ I 39239 v 439 37 L8 15 he MMH ampJ62 72 mm m 2 IQ 1622z M W m x R o A o 3X JHZ JT7tl K N E 15 39 HK 1 NM 39 ex 38 RIM I m V2 39 L 3 62 M O Q i 2 M 2 aha2X 39a L1 Z 2 Lb towgsa t M HMO amp m m Admd ol M SQ Wevdh W Max mo 4 mo 33 6amp3 i 39l Lg lt6 a 0 0 H IQ x20 W h Max 1OWQ Ll 3quot an M MAIN ample 35 4t Wtzlc I6 0 V68 2 0 m 32 23 3 M L27 4 r0 mag19quot 024 73 I11 M N75 93954 Q I 5 A 3 away9 m 5 39039 2 R39 b z 45044 5 tws hm R R2 2933 s u s 12 lb 1 150 1 v 7 7 QAvi T R o 2 42 16 50 39 39 32 MMbl Qle 4 PM ltub 10 goWQ 5M quot 2 x M PA 4 49gto MW L mm 1H 9 H ulb 43 7 QM 44646 Qx bo Rama 5 R ORUIHoMS l 2 Iv Jul 4 7 V4 32 N 433 A 002 J 409 ulllllllult J its 0 N Ddg A Dixm i 9520 O N sa oz 13 I i 5 in k wwv 9 A9 I A J n he h lOcJ Qdanlor 513 Spice Jo k KPIIITO 3J9

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