Question

For the function in Item 4, what is the average rate of change over the interval 2 < x ≤ 4?

Answer 1

The average rate of change of a function is the slope of the function

The average rate of change over the interval 2 < x ≤ 4 is 2

How to determine the average rate of the function

The function is given as:

$f(x) = 2x + 10$

The interval is given as: 2 < x ≤ 4

Start by calculating f(2) and f(4)

$f(2) = 2*2 + 10= 14$

$f(4) = 2*4 + 10= 18$

The average rate is then calculated as:

$m = \frac{f(4) -f(2)}{4 -2}$

This gives

$m = \frac{18 - 14}{2}$

$m = \frac{4}{2}$

$m =2$

Hence, the average rate of change over the interval 2 < x ≤ 4 is 2

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