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What youll do is use lhopitals rule taking the limit

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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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