Final answer:
The student's question involves calculating the average rate of change of the linear function f(x) = 5x over specified intervals and comparing these rates. Since f(x) is linear, the average rate of change is constant across any intervals, meaning the average rate of change is the same for all sections.
Step-by-step explanation:
The student is asking about the average rate of change and the comparison of this rate across different sections of the function f(x) = 5x. For any linear function like this, the average rate of change between any two points is the same because the function represents a straight line with a constant slope, which is the coefficient of x. To calculate the average rate of change for two intervals, we subtract the function values at the end and start of each interval and divide by the change in x (the length of the interval).
Part A:
Step 1: Calculate the change in function over the interval ∆f(x) = f(x2) - f(x1).
Step 2: Calculate the change in x over the interval ∆x = x2 - x1.
Step 3: Divide the change in function by the change in x to find the average rate of change (∆f(x)/∆x).
Part B:
Since the function is linear, the rates of change for any two sections will be identical. This is because the coefficient of x (5 in this case) does not change, signifying a constant rate of change, or slope. Therefore, the rate of change for Section B is not greater; it is in fact the same as Section A.