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**Unformatted text preview: **â€™- 5
Math 123 Calculusl Name: m?Â» Fall 2005 RWJ
No calculators allowed, one page of notes allowed Instructions:
0 Read questions carefully
Help me award you (partial) credit by showing your work
Note point values
Check your answers if you ï¬nish early The exam ends promptly at 9:52
Good luck! Some Possibly Useï¬tl Formulas: ". n(n+l) ". ( +1)(2 +1) ". ( +1) 2
El: 2 iÂ§12=nn 6 n Â§l3=[nn ] â€™aiï¬Ã©f$Â« P â€˜Q l RESEAW /33/1â€™/"â€"_
2.!) . x')â€™ 1.Â». . ,
O s â€œEroserï¬‚ghlllâ€ VL 1. (49 pts.) If
f(x) =x4 â€”x3 â€”3x2 +5xâ€”2 then it can be shown that @=4x3â€”3x2â€”6x+5 (xâ€”1)2(4x+5)
and f"( ) =12x2 â€”6xâ€”6â‚¬6(x-1)(2x+1p
g /
a. Where is f decreasing, if anywhere? 4â€” a (â€œM/â€˜5/â€˜f/ X jg: ( b. Where is f increasing, if anywhere? (*5/4/1) M (1,â€œ) 0. Where is f concave down, if anywhere? kFâ€”H
[" 1/1, l 3 2- d. Where is f concave up, if anywhere? (Â«pa/r) M (We) continued on next page e. State any inï¬‚ection points of f (give just the x coordinate value(s), if any). Wm: M): (-i, 40(4))
tr ( l/ LKI))
(f f. Where, if anywhere, does f take on relative maximum values (give just the x coordinate
value(s), if any)? [Um g. Where, if anywhere, does f take on relative minimum values (give just the x coordinate
value(s), if any)? clâ€™ï¬rwtkrvï¬ 2005
2. (11 pts.) Evaluate 2(71'2 â€” 31' + 5) using the results on the cover sheet of this exam.
i=1 =7 ZZâ€œâ€”3 21* 2:;
Z?â€˜ ch (:Â¢â€™ â€™ 7 (WWKWÃ©â€™XW'Q -3 @5)(â€â€â€˜) + was csâ€œ) Ã© â€™L 3. (20 pts.) Find the following: a. 17x3 +53:2 +3xâ€”4 dx c. [(7sec2xâ€”2cosx)dx : 7 S $Â¢QF -2 S 5a,.wa 4. (10 pts.) Find :17: by implicit differentiation if (x+ y)2 = x3 cosy Also, evaluate the derivative at the point (1, O). A L z A
2:foÂ«+*9)) J?â€˜ (23600] '2-(KH7>â€™(I* 6&1): ngmg 4â€” 0:36-94:79)in Arc Ax Â£12 ( "LOG-#1) + Â«59417) -,- 3â€™0)sz ~20â€) II (LC/*0) fâ€™ [9:1â€˜0 5. (10 pts.) A painting is hung ï¬‚at against an art museum wall, with its bottom and top
edges at distances 7 ft and 12 ft, respectively, above the ï¬‚oor (so that the painting is 5 ft
tall). The painting is viewed by a tourist whose eye level is 6 ft from the ï¬‚oor. The viewing angle of the painting by the tourist depends upon the/distance x she is from
the wall. In particular, it can be shown1 that the viewing angle is biggest (making the
painting appear as large as possible) when the quantity 5x
x2+6â€™ x20 f(x)= is maximized. continued on the next page 1 Nahin, Paul (2004), When Least is Best, Princeton University Press, Princeton, NJ, pp. 73-77, 147-148. V7. Determine the distance, in feet, the tourist should stand from the wall to maximize her
viewing angle of the painting. Show your work! {(WLA-Ã©) -' ;?<[2-)c) @774)"
: â€œÂ§x"+3Â° T â‚¬(Ã©._7(") â€œD
Q Hâ€” ()1 (KL1"< )L
C" x2JZ MXIWâ€˜M @ QCÂ¢Q (Ã©)! acadtwï¬ue 1; adâ€™Ã©k/ll)â€™ ï¬n WXIMV": [malt Hp)=o avg zthâ€”ao q; raw) WW imam Munâ€ 13 x42 L4: ...

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- Summer '06
- JOHNSON
- Calculus