Finding the derivative of a function is called differentiation. Basically, you calculate the slope of the line that goes throughfat the pointsxandx+h. Because we take the limit forhto 0, these points will lie infinitesimally close together; therefore, it is the slope of the function in the...
To prove that it is not possible to do anything better, we must consider all foldings, so calculations become more involved. We shall study triangles with vertices at,, and, withandvery small. This means that the side lengthsare almost proportional to. These narrow triangles will give us th...