Let R = f(t) be a function that gives the total revenue of a firm (in millions o
ID: 2890644 • Letter: L
Question
Let R = f(t) be a function that gives the total revenue of a firm (in millions of dollars) during the the current fiscal year, where t is the time in months since the start of the year. Choose the statement that correctly describes the function exc dto be positive, or negative? dR is the rate the total revenue is changing with respect to time. The units of d are millons of dollars per dt dt dt O d is the average rate of change of revenue over the fiscal year. The units of d are millions of dollars per month, d is never negative. dt dt dt 1s the month where the firm has its m aximum revenue. The units of d are millions of dollars. dR is dt dt positive d is the rate the total revenue is changing with respect to time. The units of dR month, d O are millions of dollars per dt is never negative.Explanation / Answer
As per the definition of the derivative,if f(t) is a function,then f'(t) is the rate of change of f with respect to t.so when Total revenue R is defined by f(t),then dR/dt is the rate of change in total revenue with respect to time.It is neither the average rate of change of revenue nor the total revenue for fiscal year nor the month with the maximum revenue.
hence options b,c,d are wrong.
also dr/dt could be negative or positive,which depends on the revenue function.hence option e is also wrong.
therefore by the process of elimination,option a is the correct answer which accurately states that dr/dt is the rate the total revenue isfor changing with respect to time and it could be positive or negative whose units are milliomillions of dollars per month.
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