Question

Find the average rate of change of f(x)=x2 over the interval – 4, – 2. Write your answer as an integer,or decimal rounded to the nearest tenth.

Answer 1

To find the average rate of change of the function \( f(x) = x^2 \) over the interval \([-4, -2]\), we can use the formula:

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

where \( a = -4 \) and \( b = -2 \).

First, we calculate \( f(-4) \) and \( f(-2) \):

\[
f(-4) = (-4)^2 = 16
\]
\[
f(-2) = (-2)^2 = 4
\]

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

\[
\text{Average Rate of Change} = \frac{f(-2) - f(-4)}{-2 - (-4)}
\]
\[
= \frac{4 - 16}{-2 + 4}
\]
\[
= \frac{-12}{2}
\]
\[
= -6
\]

Thus, the average rate of change of \( f(x) = x^2 \) over the interval \([-4, -2]\) is \(\boxed{-6}\).