I agree that the point $(2,2)$, is the only one that meets all criteria. Now we need to compare the value of $f$ at another point on the constraint,...
What I would do is observe that we have cyclical symmetry, that is we may interchange $x_1$ and $x_2$ with no change in either the objective function...
There are online calculators that will spit out the answer to this question, however if you want genuine help, we need to know what you've tried, or...
Well, the coefficient $a_n$ of $x^n$ in the power series reduces to $6^n$, for $6\cdot 12\cdot 18\cdots 6n = (6\cdot 1)(6\cdot 2)\cdots (6\cdot n) =...
For the sake of completion, I'll post a complete answer. Let $X$ be a first countable Hausdorff space. Fix $x\in X$, and let $\{B_n\}_{n\in \Bbb N}$...
I obtained a master's degree in mechanical engineering in May 2014.
Then I went on to join a master's programme in mathematics and obtained a master's degree in July 2016. I am currently a first year PhD student in mathematics. I love fountain pens and am a die hard fan of the Prince of Persia 2008 video game.