Chapter 0.2, Problem 21E

Cost-Benefit Let $f(x)$ be the cost-benefit function from Example 6. If $70\%$

of the pollutant has been removed, what is the added cost to remove another $5\%$? How does this compare with the cost to remove the final $5\%$ of the pollutant? (See Example 6.)

Example 6 A Cost-Benefit Model

Suppose that a cost-benefit function is given by

$f(x)=\frac{50x}{105-x},0\le x\le 100,$

Where $x$ is the percentage of some pollutant to be removed and $f(x)$ is the associated cost (in millions of dollars). (See Fig 12.) Find the cost to remove $70\%$, $95\%$ and $100\%$ of the pollutant.