I've got a school project, in which I'm supposed to get a radius of a base and a height of a cylinder while having the maximal volume possible. Surface area of the cylinder is known.
I found a great solution on this forum (https://math.stackexchange.com/a/1449593/621973), but the problem is that I need to explain my teacher, how I turned $$\frac k{(k+1)^{3/2}}$$ from V(k) into $$f(k)=\ln\frac{k}{(k+1)^{3/2}}$$ By the way, I can't give her another solution so I really need to find explanation for this one.
I'll be glad for every idea.
P.S.: Sorry for my english.