Unit 5: Analytical Applications of Differentiation

Let [math].

Let [math] on [math].

The graph of [math], the derivative of a twice-differentiable function [math], is shown below. The graph of [math] has x-intercepts at [math], [math], and [math], and the graph of [math] has a local maximum at [math] and a local minimum at [math].

Let [math] for all real numbers [math].

A farmer wants to build a rectangular pen with three parallel internal dividers (creating four equal sections), using a total of 600 feet of fencing.

The function [math] is continuous on [math] and differentiable on [math]. Selected values are given:

Let [math] be a function defined on [math]. The graph of [math], the derivative of [math], consists of two semicircles: one with center [math] and radius 3 (above the x-axis), and one with center [math] and radius 2 (below the x-axis). [math].

Let [math].

Let [math].

The table below gives values of [math], [math], and [math] at selected x-values for a twice-differentiable function [math].