BEagle,
No explanation can ever be convincing if the audience do not understand it.
The reason for my earlier post is the fact that the vast majority, and I really do mean the vast majority, of current JAR ATPL students in the UK know absolutely nothing about calculus. Many of them have great difficulty in dealing with what you and I would regard as basic arithmetic.
To understand how they would have viewed your initial explanation, we can use your statement;
I think we studied calculus at the age of 14 or 15 when I was at school - that and co-ordinate geometry were the first parts of the Additional Mathematics 'O' level syllabus.
Just cast your mind back to when you were 13 3/4 (before you first met calculus). Now imagine how convincing any explanation using differentiation would have been to you then. You may have been intrigued, you may have been impressed, but I doubt if you would have been convinced. A more probable response from many current ATPL students would be "Oh Bollox, this maths is all far too difficult, I just want to be an airline pilot".