The Slope Of a Curve:

Consider the graph:

The slope of the curve is the slope of the secant line between point A and another point P on the graph.

Notice that h can change and with it the location of point P, therefore h is the limiting factor of the slope of the curve. As h gets close to point A, the slope of the curve becomes the tangent of the graph at point A.

The tangent line of f at point A is: