Diminishing Returns. Spending money on advertising for a productcan increase the amount of revenue generated by selling thatproduct. Eventually, however, the amount by which revenue increasesis offset by the cost of the advertising. The revenue generated (inthousands of dollars) by spending x thousands of dollarsadvertising a certain product is measured and found to be
R(x) = x3e?0.3x,where x is at most 10 (that is, $10,000).
If R?(x) is negative, it means that spending more money willactually reduce sales. IsR?(x) ever negative on the interval 0 ? x? 10?
We would like to find the point at which R?(x) stops increasing.This is called the point of diminishing returns.
(a) Calculate R??(x).
(b) On what intervals is R?(x) increasing and on what intervals isR?(x) decreasing?
(c) What is the point of diminishing returns for this particularproduct?
