Hello! I've scavenged the internet and asked two professors, with no avail. I don't want to ask my professors because he does not want to give us the answer, since he wants to put it on the final.
Anyway, story aside the picture is of problem number 55 from chapter 14.7(Maximum and Minimum values) of the book "Calculus" by Stewart.
In addition to the question given by the textbook, my professor told us to 1) Prove the unique critical points exist and 2)prove there is absolute minimum at this point.
The question was given in class but he said it will be on the final so our class is scrambling to find the solution. Other professors are having trouble with it to (or in hindsight we suspect it might be they just don't want to deal with it since we aren't their students).
We found a website that answers the textbook's question, but not for the questions give by the professor: http://www.slader.com/textbook/9780538497817-stewart-calculus-7th-edition/979/exercises/55/#
Any help would be appreciated. Thank you!