Questiona) Suppose the marginal revenue function is negative between 50 and 100 . The revenue is increasing between 50 and 100. The revenuei is decreasing 50 and 100. The revenue has a maximum at 50and 100. The revenue has a minimumeat 50 and 100. Noneoof these
Studdy Solution
STEP 1
1. The marginal revenue function represents the derivative of the revenue function .
2. If is negative over an interval, it indicates that the revenue function is decreasing over that interval.
3. We are analyzing the behavior of the revenue function between and .
STEP 2
1. Interpret the meaning of a negative marginal revenue function.
2. Determine the behavior of the revenue function between and .
3. Identify if the revenue function has a maximum or minimum at the endpoints and .
4. Conclude which statement is correct.
STEP 3
A negative marginal revenue function indicates that the revenue function is decreasing over the interval where is negative. This is because the derivative of a function gives the rate of change of the function, and a negative rate of change means the function is decreasing.
STEP 4
Since is negative between and , the revenue function is decreasing over this interval.
STEP 5
To determine if there is a maximum or minimum at the endpoints and , we consider the behavior of at these points: - If is decreasing throughout the interval, it cannot have a maximum at either endpoint. - Similarly, since the function is decreasing, it cannot have a minimum at either endpoint unless the function changes direction, which is not indicated by the information given.
STEP 6
Based on the analysis:
- The revenue is not increasing between 50 and 100.
- The revenue is decreasing between 50 and 100.
- The revenue does not have a maximum at 50 and 100.
- The revenue does not have a minimum at 50 and 100.
Therefore, the correct statement is: "The revenue is decreasing between 50 and 100."
The correct statement is: "The revenue is decreasing between 50 and 100."
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