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Unformatted text preview: the surface area of a sphere of radius r is 4 πr 2 , and its volume is 4 3 πr 3 .) 4. Consider the function f ( x ) = x 2 ln x . a) (2 points) Give the interval of xvalues for which the function is deﬁned. b) (10 points) Give a mathematical justiﬁcation of the behavior of the function at each end of this interval. 4. c) (12 points) Find all relative maxima and minima of f , giving full mathematical justiﬁcation. 4. d) (8 points) Find any inﬂection points of f , giving full mathematical justiﬁcation. e) (6 points) Sketch a graph of y = f ( x ) that includes all interesting features of the curve. Include the scales used on your axes. 5. (15 points) One hallway (which is 4 feet wide) meets another hallway (which is 8 feet wide) in a rightangled corner. What is the length of the longest ladder which can be carried horizontally around the corner? Give an exact answer, assuming the ladder has no width....
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 Winter '02
 Moore
 Math, mathematical justification, lim x0 ex, Number Section Time

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