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Unformatted text preview: Name: MA 1021  2008 A Term Section 2
October 3, 2008 Quiz — Sections 3.9, 4.2, 4.3 1. Consider the function: f (x) = x4 + 4x3 — 20x2 — 2175' On which intervals, if any, is this function increasing? On which intervals,
if any, is this function decreasing? (10 points) (’60 —: LI‘XBb IZKZ’ LILOX 107;) a. '+x(x"’+ 3x— 10) pfx): Li'X (X+ s) (xii) Fesuii‘ deCPeQSI«j "S 0 Increasing d earns lr‘lj lin c (“99.3 fanj pfx) IS Intreaﬂnj on (50) ﬁnal (2,4—95), I}.
rs decrEasmj an (—o6’S) ﬁnal (0'2) 2. 2 _
Consider the function: f (x) = x 2
x + 5 On which intervals, if any, is this function increasing? On which intervals,
if any, is this function decreasing? (10 points) Use the linear approximation technique we studied this past week to
approximate each of the following. Express your answers as fractions (no
need to convert to decimal equivalents) (5 points each) am
L60 :— 1 ‘px/‘Q (x‘m) my: >3" m") 1 ‘5? l
x243 Nah: Jig“: [It
a 1%? We) = 7 1149): 71— ;‘TJrﬂs—LM)’: £084} b.33115 Lag): 100'») 'r $’(¢~)()§~6‘~) JV; 19(3): xy‘ MK)”; isx‘ I
x: 33 Man J; 37;: g;
0L2}?— «9(a): 7* 4. Differentiate both sides of the expression: 2
x
yzcosx:x2]ny+——j—
y
. dy
w1th respect to x, but do not solve for a Qj :[ﬁcosx —— 37'an X :2 1‘ (I 0 points) ...—. 30W 5 20’
x243 + 2‘73”3X25 51?? 6: 5. Find the equation of the line tangent to the curve described by
x2 y + xy2 = 2x3y3 at the point (1,1) (10 points) A rectangular box has its dimensions changing at differing rates: Its
Width is decreasing at 3 inches per second, its length is increasing at 2
inches per second, and its height is increasing at 4 inches per second. The
box is currently a perfect cube, 10 inches wide, 10 inches long, and 10
inches high. a. What will the dimensions of the box be three seconds from now? (2poz'nts) MA = lrl
PM = ’6
M3) = ’21 b. At what rate is the volume of the box changing now, at t=0? (8 points) V: 01v_ as 43 WW!
M’__}2w A++X£~A+t AF Pinkville is 40 miles Eve—st of Yellowborough. A blue car leaves
Yellowborough at noon, traveling north at 15 mph. A red truck leaves
Pinkville at 2:00 pm, traveling east at 60 mph. At 4:01 pm, the red truck
stops to pick up a purple cow hitchhiking at the side of the road. a. What color is the bear? Explain your reasoning. (2 points BONUS)
Answer; Mat); vowJ1 b. How far apart are the two cars at 4:00 pm? (4 points)
See Plc‘ine o 4:01), we blurl Car inf1' Mvtfcal
' The Fed 4'ch has jam 2x50 mics) dual 50 H"; lZO “LPG: 96 wules‘ {asi oF‘ Yellowbnnugk. AF 'i'hi‘ km, 2: \ILoH so? : 100 c. How fast is the distance between the cars changing at 4:00 pm? (Spoints)
61;:  I; 912 __ 7
0H7 A”; 3:60 "
Z .41 c 60 ﬁzz?!)
all
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x z? : X24" U ...
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 Spring '08
 TASHJIAN
 Calculus

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