Final answer:
The correct answer to the differentiation of the function f(x) = 2x is f'(x) = 2, represented as option B. The derivative signifies a constant rate of change, which aligns with the linear nature of the function.
Step-by-step explanation:
The student has asked to differentiate the function f(x) = 2x. The process of differentiation is used to determine the rate at which a function is changing at any point on its curve. It is a fundamental concept in calculus and involves finding the derivative of a function.
In this case, we are looking at a linear function, and the derivative of a linear function is particularly straightforward to calculate. The general form of a linear function is y = mx + b, where m is the slope, and b is the y-intercept. For the function f(x) = 2x, m equals 2 and there is no y-intercept since the equation does not have a constant term.
To find the derivative, or f'(x), of the function f(x) = 2x, we simply take the coefficient of x, which represents the slope of the line. Therefore, the derivative of the function is f'(x) = 2, which corresponds to option B) in the multiple choice question provided by the student.
The derivative indicates the rate of change of the function, and since f(x) = 2x is a straight line with a constant slope, the rate of change is constant across all values of x. This is a fundamental characteristic of linear functions. In terms of the graph, the line f(x) = 2x is neither horizontal nor restricted to the portion between x = 0 and x = 20 as mentioned in the provided reference information, which appears to be a discrepancy from the function being asked about.