Question

Find the average rate of change of f(x)= – 3 x over the interval – 6,2.

Answer 1

To find the average rate of change of the function \( f(x) = -3x \) over the interval \([-6, 2]\), we can use the formula for the average rate of change given by:

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

where \( a = -6 \) and \( b = 2 \).

First, we need to calculate \( f(-6) \) and \( f(2) \):

1. Calculate \( f(-6) \):
\[
f(-6) = -3(-6) = 18
\]

2. Calculate \( f(2) \):
\[
f(2) = -3(2) = -6
\]

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

\[
\text{Average Rate of Change} = \frac{f(2) - f(-6)}{2 - (-6)} = \frac{-6 - 18}{2 + 6} = \frac{-24}{8} = -3
\]

Thus, the average rate of change of \( f(x) = -3x \) over the interval \([-6, 2]\) is \(-3\).