Question

Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 0, is less than or equal to, x, is less than or equal to, 60≤x≤6.
xx f, of, xf(x)
00 9494
22 9090
44 8686
66 8282
88 7878
1010 7474

Answer 1

To find the average rate of change of a function over the interval from \( x = 0 \) to \( x = 10 \), we use the formula for the average rate of change, given by:

\[
\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}
\]

where \( a \) and \( b \) are the endpoints of the interval.

From the table provided, we can identify the values of the function at these endpoints:

- \( f(0) = 94 \)
- \( f(10) = 74 \)

Now substituting \( a = 0 \) and \( b = 10 \) into the formula:

\[
f(b) = f(10) = 74
\]
\[
f(a) = f(0) = 94
\]

Substituting these values into the average rate of change formula gives us:

\[
\text{Average Rate of Change} = \frac{f(10) - f(0)}{10 - 0} = \frac{74 - 94}{10 - 0} = \frac{-20}{10} = -2
\]

Thus, the average rate of change of the function over the interval \( 0 \leq x \leq 10 \) is:

\[
\text{Average Rate of Change} = -2
\]