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Key52010 - Math 16A(Summer 2010 Kouba Quiz 5 1(20 pts For...

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Unformatted text preview: Math 16A (Summer 2010) Kouba Quiz 5 1.) (20 pts. ) For the following function f determine all absolute and relative maximum and minimum values inflection points, and x- and y inteICepts. State clearly the open intervals for which f IS increasing (T), decreasing (i), concave up (U) and concave down (fl). Neatly sketch the g1 aph of f. f(:1:) 2 33(3: —— 3)2 on the interval [—1,5] 3., +3) = ><- 2Q<~3j+ O]CX- 51k : Q<~3) Cax+ Cx~3):( : Lx~3)[:ax,33: o 2:1: 2 ) (5 pts each) Let f(:L‘ )= 1 _ an a.) Use limits to determine equation(s) for all horizontal asymptotes. ‘ 11 1/ ‘l M &%M M 173,- ,4; l 99190 (-x 'x—aroo (“PC /;( X—atap ?—( Aé,~- v0~(v°Z/°[email protected] H"4‘24- b.) Use limits to determine equation(s) for all vertical asyniptotes. 3.) (10 pts.) Let f(:1:)=cos:c—\Bsin$. Solve f”(m)=0for 33,0gcc327r. .2 {(ij : \Mx— (ff/wax —_——=: “l3 (Bi): “MKV 63’ ~11“ 7W— ’3‘ 7("3/ /6 4.) (10 pts.) Let f(m) = 6331/3 — 7;. Set up a Sign chart for the first derivative f’. Indicate the open intervals on which f is (T) and (l) . D W: W X ”M 9 ~2 M—P‘QQ:E-}LX 4.; : .5; , if? _ 9~>< 3‘0 02 1/3 XA/3v 2/ ,. /3 X X 3 ——-> XIX :o A 3 + -+ f ——>)<J>/3:,,1—————‘e>(“«9\‘«‘8‘—%7(3‘"f0;:"a'L V o + 4204, o / Yglw~f5§<x<oj o<x<1flsj __.~1————————1———l————+——~> ... -l g - .. 39(5-fi X20 X36; \//~<)\lr/%D’W X< V??? X>Vf ...
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