You've got the answer
Now let's do some bits of algebra... remember this property :
and this :
The problem is:
given a cylinder (I prefer beer can) holding 1000 cubic cm. What should the radius and height be to minimise the surface area.
I have tried the following
subsitituting (h), and simplifying
derive that to get:
Solving for r when S'=0 (critical point), I obtain.
, which according to the text book is correct. Great news. Now I get stuck...
I cannot get h correct. For some reason h is .
I am so close yet cannot figure out how to get that result.
Subsituting r into the original equation for h gives:
This is not correct.