Question

How would I show that the minimum cost of a 100cm^3 cylinder is obtained when h/r=2 SA=2πr^2 + 2πrh using derivatives

Answer 1

at the min/max of a function, its slope is zero.
so just differentiate SA with respect to r to get SA'.
then find what value of 'r' is required to give you SA'=0.
you can confirm this represents the minimum by finding the 2nd derivative (SA'') and showing that its value is positive for the value of 'r' that makes SA' zero.

Answer 2

what abut h

Answer 3

do the math - you should get the answer. treat 'h' as a constant.