Question
Calculate the average rate of change over the interval [−2,1]
given the function f(x)=x2−3x+2
.(1 point)
Responses
12
12
−12
negative 12
4
4
−4
given the function f(x)=x2−3x+2
.(1 point)
Responses
12
12
−12
negative 12
4
4
−4
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To calculate the average rate of change of the function \( f(x) = x^2 - 3x + 2 \) over the interval \([-2, 1]\), we use the formula for the average rate of change:
\[
\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}
\]
where \( a = -2 \) and \( b = 1 \).
**Step 1: Calculate \( f(-2) \)**
\[
f(-2) = (-2)^2 - 3(-2) + 2 = 4 + 6 + 2 = 12
\]
**Step 2: Calculate \( f(1) \)**
\[
f(1) = (1)^2 - 3(1) + 2 = 1 - 3 + 2 = 0
\]
**Step 3: Substitute into the average rate of change formula**
\[
\text{Average Rate of Change} = \frac{f(1) - f(-2)}{1 - (-2)} = \frac{0 - 12}{1 + 2} = \frac{-12}{3} = -4
\]
Therefore, the average rate of change of the function \( f(x) = x^2 - 3x + 2 \) over the interval \([-2, 1]\) is \(-4\).
Final answer: **−4**.
\[
\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}
\]
where \( a = -2 \) and \( b = 1 \).
**Step 1: Calculate \( f(-2) \)**
\[
f(-2) = (-2)^2 - 3(-2) + 2 = 4 + 6 + 2 = 12
\]
**Step 2: Calculate \( f(1) \)**
\[
f(1) = (1)^2 - 3(1) + 2 = 1 - 3 + 2 = 0
\]
**Step 3: Substitute into the average rate of change formula**
\[
\text{Average Rate of Change} = \frac{f(1) - f(-2)}{1 - (-2)} = \frac{0 - 12}{1 + 2} = \frac{-12}{3} = -4
\]
Therefore, the average rate of change of the function \( f(x) = x^2 - 3x + 2 \) over the interval \([-2, 1]\) is \(-4\).
Final answer: **−4**.
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