Math Challenge - August 2019

[sage gogenkil]

Spoiler: Q 1

I got the answer as $e^{-2}$

First, I took derivative of $x^a e^{2a-x}$ and equated it with 0, and got that maximum happens when x=a or when $f(a)=(ae)^a$ . This is ofcourse, not the maximum when a is an even number.

Then, have to find the minimum of $g(x)=(xe)^x$ for which we use the same procedure to get $a=e^{-2}$.

These types of questions are great for a physics major. I'd love to look over some of the questions thanks.

 

[fresh_42]

These types of questions are great for a physics major. I'd love to look over some of the questions thanks.

In case you want to see them (at least many of them) gathered in a document, see
https://www.physicsforums.com/threads/solution-manuals-for-the-math-challenges.977057/There should be quite a few useful theorems, equations, and inequalities.