Posted: Feb 16, 2012 1:04 pm
The Hanging Monkey wrote:Well yes, "d" indicates a small change, but I don't see how small changes are relevant to working out a general relationship.
Other than that I followed the mathematics CarlPierce posted fairly easily.
You use the small change idea to find the gradient at a particular point. The idea being that the smaller and smaller the change is the better and better the answer is at a particular point. Darkc doesn't want us to discuss limits so I won't say any more on that.
The general relationship is gotten because I said 'for some X' i.e what I did will work for any value of X on the y = x^2 curve. So gives you the general relationship in terms of x.
In general for a polynominal equation you just reduce the power by 1 and multiply by the original power.
So the derivative of x^2 = 2x and the derivitive of x^3 = 3x^2 etc.