Maxima and minima problem A conical tent of the given capacity (volume) has to be constructed. Find the ratio of the
height to the radius of the base so as to minimise the canvas requried for the tent.

V = 1/3 pi r^2 h
SA = pi r s + pi r^2
Since volume is fixed and is a function of the radius of the base and the height of the cone, it suffices to find just one of those values (it will give us the other and therefore the ratio). Since those are the two variables we are concerned with, start by getting rid of that nasty slant height, s, in the second equation. Use the Pythagorean theorem to write it as root(r^2 + h^2).
I'll solve the first equation for h:
h = (3V)/(pi r^2)
plug that into the second equation and we have a (nasty) function for surface area in terms of r. 
SA = pi r root[r^2 + (3V/pi r^2)^2] + pi r^2
There's your f(r), now just differentiate it, set it to zero, solve for r values and check them to see which yields the minimum surface area.
