Objective 2.6


The graph above/below shows the Total Revenue, r(t)\displaystyle {r}{\left({t}\right)}, for the Boeing Corporation from 1990 to 2002.
Also shown is the revenue that Boeing made just from sales of its 737 airplane, a(t)\displaystyle {a}{\left({t}\right)}.

A. Based on the graphs shown r(t)a(t)\displaystyle {r}{\left({t}\right)}-{a}{\left({t}\right)} is

B. Based on the graphs shown r(t)a(t)\displaystyle {r}'{\left({t}\right)}-{a}'{\left({t}\right)} is
[hint: r(t)a(t)=(r(t)a(t))\displaystyle {r}'{\left({t}\right)}-{a}'{\left({t}\right)}={\left({r}{\left({t}\right)}-{a}{\left({t}\right)}\right)}']

C. What does the function r(t)a(t)\displaystyle {r}'{\left({t}\right)}-{a}'{\left({t}\right)} measure?


D. r(4)a(4)=0\displaystyle {r}^{'}{\left({4}\right)}-{a}^{'}{\left({4}\right)}={0}. Interpret what this means.

[hint: think (r(t)a(t))=0\displaystyle {\left({r}{\left({t}\right)}-{a}{\left({t}\right)}\right)}'={0} and what is happening to a function when its derivative is zero?]