Unit 5: Analytical Applications of Differentiation

Let [math] for all real [math].

Let [math].

The graph of [math] is shown. It consists of a semicircle of radius 2 centered at [math] (above the [math]-axis) for [math], and the line [math] for [math]. Given [math].

Find the point on the curve [math] that is closest to the point [math].

Let [math] on the interval [math].

Let [math] on the closed interval [math].

The function [math] is twice differentiable on [math]. Selected values of [math], [math], and [math] are given in the table below.