What is the average rate of change of f(x) = 2x + 1 from x = 5 to x = 10?

To find the average rate of change of the function f(x) = 2x + 1 from x = 5 to x = 10, we use the formula for average rate of change, which is:

Average Rate of Change = \( \frac{f(b) – f(a)}{b – a} \)

Here, a = 5 and b = 10.

First, we need to calculate f(5) and f(10):

• f(5) = 2(5) + 1 = 10 + 1 = 11
• f(10) = 2(10) + 1 = 20 + 1 = 21

Now, we can substitute these values into the average rate of change formula:

Average Rate of Change = \( \frac{21 – 11}{10 – 5} = \frac{10}{5} = 2 \)

The average rate of change of the function f(x) = 2x + 1 from x = 5 to x = 10 is 2.