Question

Find the average rate of change of f(x)=
–
10
x
over the interval
–
1,3.
Write your answer as an integer, fraction, or decimal rounded to the nearest tenth. Simplify any fractions.

Answer 1

To find the average rate of change of the function \( f(x) = -10x \) over the interval \([-1, 3]\), we use the formula for the average rate of change:

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

where \( a = -1 \) and \( b = 3 \).

First, we need to calculate \( f(-1) \) and \( f(3) \):

1. Calculate \( f(-1) \):
\[
f(-1) = -10(-1) = 10
\]

2. Calculate \( f(3) \):
\[
f(3) = -10(3) = -30
\]

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

\[
\text{Average Rate of Change} = \frac{f(3) - f(-1)}{3 - (-1)} = \frac{-30 - 10}{3 + 1} = \frac{-40}{4} = -10
\]

Therefore, the average rate of change of \( f(x) = -10x \) over the interval \([-1, 3]\) is \(\boxed{-10}\).