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Unformatted text preview: o. What you'll do is use l'Hopitals rule (taking the limit at x goes to 0) to find that f (x) is (well, should be) 0 at x = 0. Don't do the second derivative test unless you have a few hours to spare! Notice that f (x) is positive (same reasoning as above) for numbers really close to 0 on both the positive and negative sides of x = 0, so that f (x) is increasing through x = 0 so that we have an inflection point. 1 Or use a computer to draw the graph. This program is called Mathematica. f [x] = x 3/(Log[1 + x 2])
x3 Log[1+x2 ] Here's the graph for x between 5 and 5 (it looks like there is a critical (inflection) point near x = 0: Plot[(x 3)/(Log[1 + x 2]), {x, 5, 5}] 40 20 4 2 20 2 4 40
Graphics Here is the graph really close up: Plot[(x 3)/(Log[1 + x 2]), {x, .0001, ....
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This note was uploaded on 07/11/2009 for the course MATH Math 31B taught by Professor Houdayer during the Winter '09 term at UCLA.
 Winter '09
 HOUDAYER
 Math, Approximation, Taylor Series

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