Final answer:
The units of f′(x) are dollars per meter. Option A is correct.
Step-by-step explanation:
The units of f′(x) can be determined by looking at the relationship between the quantities in the given scenario. In this case, f(x) represents the cost in dollars and x represents the amount drilled in meters. The derivative, f′(x), represents the rate of change of the cost with respect to the amount drilled. Therefore, the units of f′(x) would be dollars per meter, so the correct answer is a) Dollars per meter.
The student has asked about the units of f'(x), which is the derivative of a function representing the cost of drilling x meters for an oil well. The derivative f'(x) represents the rate of change of cost with respect to the number of meters drilled. Therefore, the units for f'(x) would be dollars per meter, as it denotes how many additional dollars are required for each additional meter drilled.