Question

Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 1 < x < 4. x f(x) 1 1 12 2 21 3 30 4 39 5 48

Answer 1

Barbara, this is the solution:

We have the interval:

1 ≤ x ≤ 4,

therefore, the values of x included in the interval are:

• 1

,

• 2

,

• 3

,

• 4

Now, for calculating the average rate of change, we use the following formula:

Highest value of f(x) within the interval - Lowest value of f(x) within the interval/Number of values of x in the interval.

Replacing with the values we know:

• Average rate of change = (39 - 12)/4

,

• Average rate of change = 27/4

,

• Average rate of change = 6.75