The figure shows graphs of the marginal revenue function R ' and the marginal cost function C ' for a manufacturer. (Recall from Section 4.7 that R(x) and C(x) represent the revenue and cost when x units are manufactured. Assume that R and C are measured in thousands of dollars.)
R'(x) is above C'(x) between x=50 and x=100
Use the Midpoint Rule to estimate the value of this quantity in thousands of dollars.
To estimate the value using the Midpoint Rule, we need to find the average value of the difference between R'(x) and C'(x) over the interval [50, 100].
1. Calculate the midpoint of the interval [50, 100]:
Midpoint = (50 + 100) / 2 = 75
2. Evaluate R'(x) and C'(x) at the midpoint:
R'(75) and C'(75)
3. Subtract C'(75) from R'(75) to find the difference:
Difference = R'(75) - C'(75)
4. Multiply the difference by the width of the interval:
Approximate value = Difference * (100 - 50)
The approximate value of this quantity will be in thousands of dollars.