Help with inequality in three variables subject to one constraint
Let $a,b,c>0$ such that $a+b+c=3$, find max/min of $\frac1{a^2+1}+\frac1{b^2+1}+\frac1{c^2+1}$
Clever bounty reputation hack I say "hack" in the most favorable light. It's a clever idea and theoretically beneficial.  I noticed that an old question of mine suddenly started getting a lot of renewed attention. The question had been answered, with an answer accepted. But another user added a well reasoned and insightful answer to the list. He also opened a +100 bounty on that question.  The resulting increased attention quickly got his answer quite a lot of up-votes. Well more than the 100 points he had spent on the bounty. Therefore, he gets a net rep profit out of the transaction.  So here's the hack:   Find an interesting question Research and provide a very good answer Open up a bounty on that question to attract attention and votes to your new answer Profit!!!   2 and 3 may be out of order--I didn't see the timing of it. But either way, assuming he gets more than 10 votes, he still gets increased rep out of the deal.  I don't think this is necessarily bad for SO - it does generate some useful discussion and insightful answers. Plus you can increase your own rep very rapidly by making your answers highly visible, and therefore frequently voted upon.   However, it does slightly change the meaning and purpose of bounties away from starting a discussion and toward self-promotion. Still, interesting. com.google.android.trichromelibrary causes many Android apps to crash Better explanation of the common general relativity illustration (stretched sheet of fabric) Does D&amp;D 5E have a mechanic similar to  or  as it exists in D&amp;D 3.5?  To put it simply, in D&amp;D 3.5, touch AC excludes armor bonuses when armor can't help against an attack, and flatfooted AC excludes your Dexterity bonus when you haven't acted yet in combat. What is wrong with "Where should this car be parked?"? Permanent xmodmap in Ubuntu 13.04 I cannot make xmodmap run on login in Ubuntu 13.04. I have searched around, including in askubuntu and all answers I found do not work.  I have a file named .Xmodmap in my home folder which contains the desired mappings. If I run it manually it works fine, so there is no error there. In order to make it run on startup, I have tried:     Using various .xinitrc containing one of the following commands:      xmodmap .Xmodmap xmodmap ~/.Xmodmap   /usr/bin/xmodmap /home/NAME/.Xmodmap if [ -s ~/.Xmodmap ]; then xmodmap ~/.Xmodmap fi  Using .Xresources instead of .xinitrc with the same variations. Setting it as a startup application.   None of the above works in Ubuntu 13.04 (64-bit). I also saw a few ideas about globally changing the keyboard mappings, but most of them were not applicable in Ubuntu 13.04 (i.e. the corresponding files did not exist where specified) and I prefer not to touch the global settings anyway. S(x), which stands for “x is a surgeon”  P(x, y), which stands for “x is a patient of y”  R(x), which stands for “x recovers”  H(x), which stands for “x is happy”  1>"A surgeon with no patients is happy" means: for any person xx, if xx is a surgeon and there is no person yy for which yy is a patient of xx, then xx is happy.  2> "A surgeon is happy if all her patients recover" means: for any person xx, if xx is a surgeon and - if for every person yy for which yy is a patient of xx, we have that yy recovers - then xx is happy.  I have these as solution:  1:∀(x) ( S(x)∧ ∀(y)P(y,x) → H(x) ) 2: ∀(x) [ { S(x)∧ (∀(y)P(y,x) ∧ R(y)) } → H(x)]  Are these okay?  And how do prove that 1 follows from 2 by resolution (not by drawing a truth table)? I am trying to make a floor plan for my office, have managed to make all of the rectangular components (e.g. the rooms) however some of the desk layouts are circular and I haven't been able to work out how to make exact and measured circles. They need to have a radius of 1.45m. Why do Lagrange Multipliers work? I know that the Lagrange multiplier method helps us evaluate critical points of $f$ on the closed boundary of the restriction.   In other words we solve:$$\nabla f=\lambda \nabla g$$  But why does this method actually work? Can someone please give me an explanation. Thank you! QGIS 2.0 - can't select items in Print Composer line segment joining two centers of circles is perpendicular to line segment joining two intersection point of the circles Why doesn't the Related question list show that questions are closed? Is calling a linear-equation a linear-function, misnomer or completely wrong? From my college life, I remember many professors used to call a linear-equation a linear-function, however:  A standard definition of linear function (or linear map) is:  $$f(x+y)=f(x)+f(y),$$ $$f(\alpha x)=\alpha f(x).$$  Where as linear equation is defined as:  $$f(x)=mx+b.$$  So, linear-equation is NOT a linear-function, according to the definitions defined above.  Though, for $b=0$ the linear-equation becomes a linear-function, but it is not true in general.  Question: Is it misnomer to call a linear-equation a linear-function, or it is completely wrong to say that? And linear-equation must be considered strictly as an affine-mapping. Regular expression to match a line that doesn't contain a word I know it's possible to match a word and then reverse the matches using other tools (e.g. grep -v). However, is it possible to match lines that do not contain a specific word, e.g. hede, using a regular expression?   Input:  hoho hihi haha hede   Code:  grep "&lt;Regex for 'doesn't contain hede'&gt;" input   Desired output:  hoho hihi haha Can I exchange limit and differentiation for a sequence of smooth functions? Let $(f_n)_{n\in \mathbb N}$ be a sequence of smooth functions converging to some $f$.  Under what circumstances can I exchange limit and derivative?, i.e.  $$\lim_{n\rightarrow \infty} \frac{\partial f_n(x)}{\partial x} = \frac{\partial f(x)}{\partial x}$$ Simple question, but one that I've been curious about...is there a functional difference between the following two commands?  String::class String.class   They both do what I expect -- that is to say they return Class -- but what is the difference between using the :: and the .?  I notice that on those classes that have constants defined, IRB's auto-completion will return the constants as available options when you press tab after :: but not after ., but I don't know what the reason for this is... Exploiting JavaScript's eval() method How to restrict some websites in Ubuntu 14.04 Add a link to the timeline of a post For the past year I have been quite active on SO and a bit on meta, but I had never heard of the timeline of a post until today in a comment on meta.  There was an  two years ago of this feature as "experimental". ( for that question).  This feature was , answer: this exists, but the link has to be built manually.  I think this could be quite interesting sometimes and I would like to use this, but I will not do so if I have to build the link each time by myself.  This feature has existed for two years and is still "experimental"? Who is using it? Who knows about it?  My feature request: Implement a link in the posts to their timeline. I am sure this nice feature will be used. Determine whether or not a point lies within a rotated rectangle