Question

Find the average rate of change over the given interval. f(x) = 2x, (3,5) .

a) 1
b) 2
c) 3
d) 4

Answer 1

The average rate of change of the function f(x) = 2x over the interval (3,5) is calculated using the formula for average rate of change, resulting in an answer of 2.

Step-by-step explanation:

The question asks to find the average rate of change of the function f(x) = 2x over the interval from x = 3 to x = 5. To calculate the average rate of change, we use the formula:

Average rate of change = ∆f(x) / ∆x = (f(5) - f(3)) / (5 - 3)

Substituting the given function into the formula:

Average rate of change = (2(5) - 2(3)) / (5 - 3) = (10 - 6) / 2 = 4 / 2 = 2

Therefore, the average rate of change of the function over the interval (3,5) is 2, which corresponds to answer choice (b).