Well I've had my silly 1st year lecture today, and I thought that I'd compare it with what I recall 1st year lectures of my course :)
Well at one point we came to a point where we had to work out when some value was at a minimum. So... as you do he introduced differentials to the scene. He then apologised lots that he was doing this to us, and although he was quite sure we would have all seen them before, if we hadn't, just learn the aswer, don't bother knowing how to do it :) He then preceded to differentiate the simple function wrong, which was veyr funny. This is nothing like my 1st year electronic engineering. Here were we thrown in the deep end of differentiate this hard minging function.
But then there was a simularity to my degree - the shortcut! After all this he then crap he then said that there was a simple method to it... and this was to look at where the lines on a graph cross and that that point was always the minimum... which was quite obvious (to be honest) bearing in mind that one line did this \ and the other did that /. So he then proved that this was infact gave the correct answer... why when differention is ever used does this always happen?... well you could do it the hard way as I've shown, but make this equal this and then wham there's your answer. Hehe.