Question

Find the average rate of change over the interval [-3,0] for the function f(x)=x2−2x+4
.(1 point)
Responses

-5
-5

15
1 fifth

5
5

−15

Answer 1

To find the average rate of change of the function \( f(x) = x^2 - 2x + 4 \) over the interval \([-3, 0]\), we can use the formula for the average rate of change:

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

where \( a = -3 \) and \( b = 0 \).

1. Calculate \( f(-3) \):

\[
f(-3) = (-3)^2 - 2(-3) + 4 = 9 + 6 + 4 = 19
\]

2. Calculate \( f(0) \):

\[
f(0) = (0)^2 - 2(0) + 4 = 0 - 0 + 4 = 4
\]

3. Now substitute \( f(-3) \) and \( f(0) \) into the average rate of change formula:

\[
\text{Average Rate of Change} = \frac{f(0) - f(-3)}{0 - (-3)} = \frac{4 - 19}{0 + 3} = \frac{-15}{3} = -5
\]

Thus, the average rate of change of the function over the interval \([-3, 0]\) is \(-5\).

So, the correct response is:

\(-5\)