As h gets small, point B gets closer to point A, and the line joining the two gets closer to the REAL tangent at point A. Calculating the gradient between points A & B is not too hard, and if we let h -> 0 we will be calculating the true gradient.

The point A is at x=3 (originally, but it can be moved!)[br]What is the gradient of the line AB when h = 2?[br]h=1?[br]h=0.1?[br]h=0.01?[br]h=0? (!)[br][br]The original curve is f(x)=x³. What function would give you the gradient at any point?