Question

For the function f(x) given in the table, find the average rate of change over each specified interval. x 0 2 2.5 3 3.8 4 5 f(x) 18 15 17 12 19 17 23 (a) [2, 5]

Answer 1

The average rate of change for the function f(x) over the interval [2, 5] is calculated using the values from the table and is approximately 2.67.

Step-by-step explanation:

To find the average rate of change of a function f(x) over the interval [2, 5], we can use the formula:

Average Rate of Change = ∆f(x) / ∆x = (f(5) - f(2)) / (5 - 2)

From the table, we have:

• f(2) = 15
• f(5) = 23

Substitute these values into the formula:

Average Rate of Change = (23 - 15) / (5 - 2) = 8 / 3 ≈ 2.67

Therefore, the average rate of change of the function f(x) over the interval [2, 5] is approximately 2.67.