ABSTRACT
In this chapter we approximate functions of one variable by using the first and second derivatives and apply this to complete the proof of Proposition 21 and to give a geometrical interpretation of absolute curvature. The details are rather technical but cannot be avoided. In our case we decided to allow the methods of linear approximation to be absorbed before moving to quadratic approximation. We begin by recalling the one variable linear case. If φ is differentiable, then
φ(x + ∆x) = φ(x) + φ′(x) · ∆x + g(x,∆x) · ∆x where g(x,∆x) → 0 as ∆x → 0.
