Timeline for Why "plug in numbers" when solving inequality?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| May 17, 2019 at 13:30 | answer | added | JTP - Apologise to Monica | timeline score: 0 | |
| May 27, 2016 at 14:53 | comment | added | Dave L Renfro | Also, an obvious drawback to the first method is that the possibilities needed to examine grow at an exponential rate as a function of the number $n$ of factors. For example, with $6$ factors there are $2^6 = 64$ sign permutations, $32$ of which lead to a positive product and $32$ of which lead to a negative product. For the second method, the number of possibilities needed to examine only grows linearly (in fact, not something like $200n$ or $37n,$ but just $n).$ | |
| May 27, 2016 at 14:49 | comment | added | Dave L Renfro | FYI, in high school we used your first method, and I believe this method was the only one described in our textbook -- Dolciani's Modern Algebra and Trigonometry. I don't know where I learned about the other method, but it was after high school, and when I learned the other method we didn't plug numbers into the intervals but rather determined the sign by algebraic considerations (e.g. factor(s) corresponding to the interval) or by graphical considerations (e.g. $(e^x - 2)\ln x$ is negative just to the right of $0$ and positive for large $x).$ | |
| May 27, 2016 at 5:35 | vote | accept | CommunityBot | moved from User.Id=2139 by developer User.Id=3 | |
| May 27, 2016 at 4:53 | answer | added | user797 | timeline score: 11 | |
| May 26, 2016 at 13:47 | comment | added | Sue VanHattum♦ | Students are often poor at reasoning. Plugging in a value may feel easier to them than analyzing how many factors are negative. | |
| May 26, 2016 at 13:04 | comment | added | Amy B | It would seem that this is an extension of how linear inequalities are taught in high school. Students prefer to continue a method that they know rather than learn a new method. | |
| May 26, 2016 at 10:50 | comment | added | Git Gud | I really don't expect it to be for any reason other than the IVT. | |
| May 26, 2016 at 8:56 | history | asked | user2139 | CC BY-SA 3.0 |