The ebook Elementary Calculus is based on material originally written by H.J. Keisler. For more information please read the copyright pages.


Example 3

Suppose that by investing t dollars a company can produce

02_differentiation-364.gif02_differentiation-363.gif

items, and that it can sell x items for a total profit of

 

Find 02_differentiation-365.gif, which is the marginal profit with respect to the amount invested.

We have

02_differentiation-366.gif

By the Chain Rule,

02_differentiation-367.gif

Thus after t dollars have been invested, an additional dollar invested will bring 0.7 — t/5000 dollars of additional profit.


Last Update: 2006-11-15