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Quiz3num1soln - Math21a Quiz#3 Dec 4 2007 See 5-6pm Print...

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Unformatted text preview: Math21a Quiz#3 Dec 4, 2007 See 5-6pm Print Your Name ____%%~____ _._.__ Sign Your Name _M 0 You have 30 minutes. 0 Each problem is worth 10 points. 0 Showing as much work as possible will guarantee the most credit. 0 Partial credit will be given 1. Find the extreme values of the function and Where they occur. y=e$—e‘$ . __‘| 6x tame Va/UCS occur, wAem y/JO) y, 15 UM(/€{,V;e£)/ or @ [you/5dr?! [00151715 . n07l€ 7 I5 JefineJ for a// >r/ so ‘Mére 67/! n0 [Deana/r7 foo/317%. y : 6 re WLICA "5 O’CFI.HIJ (VEI‘XWAC’II’, and nave,“ Zcfo' So “‘6“ are my exwlremc Va/Ué’fi 2. Assume that f is continuous on [a,b] and differen- tiable on (a,b). Also assume that f (a) and f (b) have opposite signs and that f’ 7é 0 between a and b. Show that f (x) = 0 exactly once between a and b. by In4€rm€oku¥e Val/U6 TACOICM 7L4 ‘5'8 811's?! 4 C 6 (a [9) ML ‘H-ML {m = 0, I “Mr: can“; [>6 (late 5064 #‘m% Ole-(“16) ? {Vt/>30} 07lfl/Prvw'98 (>7 74‘: Mam Vet/Vt Theo/rem‘F )‘MP’C fos/s 0: 896-40 or (90’) , ma 0 MA Heal We) = £7.77“ 3 0 which IIS 01 (onVZfadIUlIIOM 1[0 {I *0' 3. You are given the first derivative of a continuous function y = f(:1:). Find 3;” and then use the steps taught in chapter 4 to sketch the general shape of the graph of f. I __ 2'55' __ —2$ iffL‘ S 0 (Do/<5 like y " ‘ 2m ifcc > 0 , - ‘ < 0 ( . \/// : Z ‘lf X no‘lfi Y/ Is no?! JiffercMQé ’2. f x >0 @ X :0 a/Val 7’ :0 174 my”; //:'2 :7 CD y vie» X4< y”: L :7 CU WLen X>C 7/20 (5) x:.0 :7 horizofi/a/ afar 4. A 1125 ft3 open—top rectangular tank With a square base :6 ft on a side and 3/ ft deep is to be built with its top flush With the ground to catch freshmen. The costs associated with the tank inVlove not only the ma- terial from which the tank is made but also an excavation charge proportional to the product my. If the total cost is c = 5(5132 + 4xy) + ley What values of ac and y will minimize it? max : x17 : ’lZS'F7l3 :7 y: {€f €0.57! : gx1+20x7 1“ /0X7/ (03% a 5x1 + 30x/ ’42... ~ I 2 7%) C 15x1+30fl3§l : 5x Area-bx g; le _ 23720 x 37750 =7 x3 2 3576’ ’ I ’: ____’_/ ’0 x7 /0;( XL ...
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