Consider the functions [math] and [math]. These are continuous and differentiable for [math]. In this problem we use the Racetrack Principle to show that one of these functions is greater than the other, except at one point where they are equal.

(a) Find a point [math] such that [math].   [math]

(b) Find the equation of the tangent line to [math] at [math] for the value of [math] that you found in (a).
[math]

(c) Based on your work in (a) and (b), what can you say about the derivatives of [math] and [math]?
[math] [math] for [math], and
[math] [math] for [math].

(d) Therefore, the Racetrack Principle gives
[math] [math] for [math], and
[math] [math] for [math].