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Quiz3num1

# Quiz3num1 - F y ′ = 2 | x | = − 2 x iF x ≤ 2 x iF...

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Math21a Quiz#3 Dec 4, 2007 Sec 5-6pm Print Your Name Sign Your Name You have 30 minutes. Each problem is worth 10 points. Showing as much work as possible will guarantee the most credit. Partial credit will be given 1

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1 . Find the extreme values of the function and where they occur. y = e x e x 2
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 negationslash = 0 between a and b . Show that f ( x ) = 0 exactly once between a and b . 3

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3 . You are given the first derivative of a continuous function y = f ( x ). Find y ′′ and then use the steps taught in chapter 4 to sketch the general shape of the graph of
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Unformatted text preview: F. y ′ = 2 | x | = − 2 x iF x ≤ 2 x iF x > 4 4 . A 1125 ft 3 open-top rectangular tank with a square base x ft on a side and y ft deep is to be built with its top Fush 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 xy . If the total cost is c = 5( x 2 + 4 xy ) + 10 xy what values of x and y will minimize it? 5...
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