# Calculus/algebra question **URL:** \ **Category:** Factual Questions\ **Created:** [November 7, 2001, 9:00am UTC](https://boards.straightdope.com/t/calculus-algebra-question/91980 "2001-11-07T09:00:22Z")\ **Posts on this page:** 6\ **Page:** 1
**Author:** ![BabaBooey](https://avatars.discourse-cdn.com/v4/letter/b/dfb087/32.png) [@BabaBooey](https://boards.straightdope.com/u/BabaBooey)\ **Post date:** [November 7, 2001, 9:00am UTC](https://boards.straightdope.com/t/calculus-algebra-question/91980/1 "2001-11-07T09:00:22Z")
OK I have this ridiculous algebra problem that’s resulted from a relatively simple calculus problem (graph function with min/max, concavity, etc…). Well, I took the second derivative of the function (x^2)/(x^3 + 1) and got up to this: (x^3 + 1)^2 (-4x^3 + 2) - 6x^2 (x^4 + 2x)(x^3 + 1) Now I have to solve for x with the function equal to zero. My classmates and I have spent a lot of time on this and the furthest any of us have gotten is 2x^9 + 6x^8 - 2x^6 - 20x^3 + 2 = 0 This is actually part of a take home test that we’ve been working on for quite a while. I know that I can look at the graph and see where the inflection points are but we need to show work for this. If anyone could help us out with either part of the problem it would be greatly appreciated, though some of you geniuses may be better off starting with the pre-simplification part because in all likelyhood we messed up somewhere on the way . ---
**Author:** ![Popup](https://avatars.discourse-cdn.com/v4/letter/p/94ad74/32.png) [@Popup](https://boards.straightdope.com/u/Popup)\ **Post date:** [November 7, 2001, 9:16am UTC](https://boards.straightdope.com/t/calculus-algebra-question/91980/2 "2001-11-07T09:16:25Z")
> [@](#): > > \*Originally posted by BabaBooey \* > \*\*OK I have this ridiculous algebra problem that’s resulted from a relatively simple calculus problem (graph function with min/max, concavity, etc…). Well, I took the second derivative of the function (x^2)/(x^3 + 1) and got up to this: > \*\* Just a quick thought… If you want to minimize the x[sup]2[/sup]/(x[sup]3[/sup]-1), Won’t that be the same as maximize the inverse? Look at (x[sup]3[/sup]-1)/x[sup]2[/sup] = x - 1/x[sup]2[/sup] instead! ---
**Author:** ![Firx](https://avatars.discourse-cdn.com/v4/letter/f/c2a13f/32.png) [@Firx](https://boards.straightdope.com/u/Firx)\ **Post date:** [November 7, 2001, 10:10am UTC](https://boards.straightdope.com/t/calculus-algebra-question/91980/3 "2001-11-07T10:10:10Z")
I see now that this was just some nefarious ploy to get me to waste time in IMHO. Well, I have a special punishment in store for the likes of you. Guards! Seize him! ---
**Author:** ![Achernar](https://avatars.discourse-cdn.com/v4/letter/a/e274bd/32.png) [@Achernar](https://boards.straightdope.com/u/Achernar)\ **Post date:** [November 7, 2001, 11:50am UTC](https://boards.straightdope.com/t/calculus-algebra-question/91980/4 "2001-11-07T11:50:53Z")
I haven’t seen the other thread **Firx** mentions, so this may be better answered there, but you can factor an (x[sup]3[/sup] + 1) out of that pre-simplified expression. That should leave you with something that’s quadratic on x[sup]3[/sup]. I’m not sure where that 6x[sup]8[/sup] came from, but it shouldn’t be there. ---
**Author:** ![bibliophage](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bibliophage/32/7615_2.png) [@bibliophage](https://boards.straightdope.com/u/bibliophage)\ **Post date:** [November 7, 2001, 2:51pm UTC](https://boards.straightdope.com/t/calculus-algebra-question/91980/5 "2001-11-07T14:51:45Z")
Starting the same thread in two different forums is called cross-posting and is not allowed here. In the future, if you suspect you have posted in the wrong forum, please e-mail a moderator to move it for you. bibliophage moderator GQ ---
**Author:** ![Firx](https://avatars.discourse-cdn.com/v4/letter/f/c2a13f/32.png) [@Firx](https://boards.straightdope.com/u/Firx)\ **Post date:** [November 7, 2001, 9:08pm UTC](https://boards.straightdope.com/t/calculus-algebra-question/91980/6 "2001-11-07T21:08:02Z")
By the way, here is a [link](http://boards.straightdope.com/sdmb/showthread.php?threadid=97613) to the other, now deceased, thread. > [@](#): > > _Originally posted by BabaBooey, in the other thread:_ > Thanks a lot. It’s not a hard problem at all, but that algebra is a pain in the ass. I’m lucky that you have mad skills. That’s 20 points on the test that you helped me get. One more thing. I had another problem where I kept plugging numbers to the left and right of critical points into the original function to find whether the function in those areas was increasing or decreasing, but I was getting some wrong answers (I was comparing my results with a graph of the function on a TI-86). Then I started plugging the numbers into the derivative of the function and everything was coming out right. I remember being tought to plug the numbers into the original function, but I haven’t seen this stuff in over a year. Which is it? To find out what the function is doing, use the derivative for increasing/decreasing and the second derivative for concavity.