The metatheorem of calculus is that almost any function looks like a straight line when we zoom in far enough. [br]When we have zoomed in far enough we cannot tell the difference between the graph and the tangent line.[br]If we have zoomed in that far we can approximate the tangent line with a secant line.[br]The slope of that line is the derivative at that point.

This applet zooms in on y=f(x) around the point A.[br]A is a draggable point.[br]The box extends out from A by a distance of zoom up and down, right and left.[br]In the zoom window you can also see the secant line using A and a point zoom/2 to the right of A.