An open-topped cylindrical glass jar is to have a given capacity. Find the ratio of height to diameter if the area of glass is a minimum.
You need surface area in terms of a single variable, in order to easily differentiate,
so we can write h "in terms of" r.
The jar volume is
It's surface area is
To find the minimum surface area, differentiate surface area with respect to r
and set it to zero.
If this is zero then
corresponds to the jar being unrealistically stretched
into an "invisible" line.