## Calculus: Early Transcendentals 8th Edition

(a) $A'(x) = \frac{xp'(x)-p(x)}{x^2}$ If $A'(x) \gt 0$, then the average productivity of the workforce would increase if more workers were added. Therefore, the company would want to hire more workers in order to improve the average productivity of the workforce. (b) If $p'(x)$ is greater than the average productivity, then $A'(x) \gt 0$
(a) $A(x) = \frac{p(x)}{x}$ $A'(x) = \frac{xp'(x)-p(x)}{x^2}$ If $A'(x) \gt 0$, then the average productivity of the workforce would increase if more workers were added. Therefore, the company would want to hire more workers in order to improve the average productivity of the workforce. (b) Suppose $p'(x)$ is greater than the average productivity. Then: $p'(x) \gt \frac{p(x)}{x}$ $xp'(x) \gt p(x)$ $xp'(x) - p(x) \gt 0$ $\frac{xp'(x) - p(x)}{x^2} \gt 0$ $A'(x) \gt 0$