Final answer:
R'(100) = 1400 represents the marginal revenue from selling the 100th unit, indicating an approximate $1400 increase in total revenue from selling one more unit, essential for business decisions.
Step-by-step explanation:
In the context of the revenue function R(x), where x represents the number of units sold, R'(100) = 1400 represents the marginal revenue when the 100th unit is sold. This means that when the sales increase from 100 to 101 units, the expected increase in total revenue is approximately $1400. The concept of marginal revenue is crucial in business and economics as it indicates how much revenue the sale of one additional unit will generate, which is essential for making informed production and pricing decisions.
To understand this further, let's consider an example using a table to illustrate changes in total revenue. If total revenue increases from $1200 to $2200 when output increases from 1 to 2 units, the marginal revenue (MR) of the second unit can be calculated as:
MR = $2200 - $1200 = $1000
Similarly, R'(100) = 1400 could be thought of as the change in total revenue from selling unit 100 to unit 101.