Calculate the average rate of change over the interval [−2,1]

Question

given the function f(x)=x2−3x+2
.(1 point)
Responses

−4
negative 4

4
4

12
12

−12

Answer 1

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:

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

where \( a = -2 \) and \( b = 1 \).

First, we need to evaluate \( f(-2) \) and \( f(1) \).

1. Calculate \( f(-2) \):

\[ f(-2) = (-2)^2 - 3(-2) + 2 = 4 + 6 + 2 = 12 \]

2. Calculate \( f(1) \):

\[ f(1) = (1)^2 - 3(1) + 2 = 1 - 3 + 2 = 0 \]

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

\[ \text{Average Rate of Change} = \frac{f(1) - f(-2)}{1 - (-2)} = \frac{0 - 12}{1 + 2} = \frac{-12}{3} = -4 \]

So, the average rate of change over the interval \([-2, 1]\) is:

\[ \boxed{-4} \]