1021 quiz 4 A Term 2008 answers

1021 quiz 4 A Term 2008 answers - Name: MA 1021 - 2008 A...

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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‘XB-b 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 fan-j 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 hitch-hiking at the side of the road. a. What color is the bear? Explain your reasoning. (2 points- BONUS) Answer; Mat); vow-J1 b. How far apart are the two cars at 4:00 pm? (4 points) See Plc‘ine o 4:01), we blurl Car inf-1' Mvtf-cal ' 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 '2. x z?- : X24" U ...
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This note was uploaded on 10/13/2009 for the course MA 1021 taught by Professor Tashjian during the Spring '08 term at WPI.

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1021 quiz 4 A Term 2008 answers - Name: MA 1021 - 2008 A...

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