To find the average rate of change of the function \( f(x) = x^2 - 2x + 4 \) over the interval \([-3, 0]\), we 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 \( b = 0 \).
- First, we calculate \( f(-3) \):
\[ f(-3) = (-3)^2 - 2(-3) + 4 = 9 + 6 + 4 = 19 \]
- Next, we calculate \( f(0) \):
\[ f(0) = (0)^2 - 2(0) + 4 = 0 - 0 + 4 = 4 \]
- Now, we plug these values 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 \( f(x) = x^2 - 2x + 4 \) over the interval \([-3, 0]\) is \(-5\).
Therefore, the answer is:
-5
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