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Project 29 MAC 2233 1. Examine the function h ( x ) = 3 ln( x ) x . What are its domain and intercepts ? Domain x > 0 ; intercept ( 1 , 0 ) Calculate h 0 ( x ) , and h 00 ( x ) . Use a number line to determine the interval(s) on which the function is increasing/decreasing, concave up/down. Are there any local extrema? inﬂection points? inc ( 0 ,e ) dec ( e, ∞ ) conc up ( e 3 / 2 , ∞ ) conc dn ( 0 ,e 3 / 2 ) Now sketch the function h ( x ) below on the axes labeled A . Include intercepts, local extrema, inﬂection points, and asymptotes. Note that lim x →∞ h ( x ) = 0 A B 2. If a metal cable of radius r is covered by insulation, so that the distance from the center of
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This note was uploaded on 12/27/2011 for the course MAC 2233 taught by Professor Smith during the Spring '08 term at University of Florida.
- Spring '08