Differentiation from first principles
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!)
What is the gradient of the line AB when h = 2?
h=1?
h=0.1?
h=0.01?
h=0? (!)
The original curve is f(x)=x³. What function would give you the gradient at any point?