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Unformatted text preview: Name: ____________________ Math 160 Final Exam Take-home portion Calculators are permitted. Please show all necessary steps, including setting up integrals. Part I (Test 2) 1. Use the definition of the derivative (i.e., the four step process) to find the derivative of the function f x = x 3 x Part II (Test 3) 2. A company manufactures open-cover boxes with square bases. (The box has no top, but it does have a square bottom, and rectangular sides.) These boxes must contain a volume of 108 cubic inches. Find the dimensions of the box that will minimize the amount of material used to construct the box. 3. Sketch the graph of a continuous function with the following properties: lim x f x = 2 lim x f x = x (-, a ) a ( a , b ) b ( b , c ) c ( c , d ) d ( d , e ) e ( e , f ) f ( f ,) f '( x ) + + + n.d. + + + + f ''( x ) + n.d. + + + + Identify local extrema and points of inflection. EC: A conical tank has a diameter of 4m and a height of...
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