Chapter 2.4, Problem 41ES

A manufacturer of athletic footwear finds that the sales of their ZipStride brand running shoes is a function $f\left(p\right)$ of the selling price $p$ (in dollars) for a pair of shoes. Suppose that $f\left(120\right)=9000$ pairs of shoes and $f^{\prime }\left(120\right)=-60$ pairs of shoes per dollar. The revenue that the manufacturer will receive for selling $f\left(p\right)$ pairs of shoes at $p$ dollars per pair is $R\left(p\right)=p\cdot f\left(p\right)$ . Find $R\text{'}\left(120\right)$ . What impact would a small increase in price have on the manufacturer’s revenue?