Question

Calculate the average rate of change over the interval [-2,1] given the function f(x)=x2−3x+2

Answer 1

To calculate the average rate of change of the function \( f(x) = x^2 - 3x + 2 \) over the interval \([-2, 1]\), we can use the formula for average rate of change, which is given by:

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

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

First, we need to evaluate \( f(a) \) and \( f(b) \).

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 we can use these values to find the average rate of change:

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

Therefore, the average rate of change of the function \( f(x) = x^2 - 3x + 2 \) over the interval \([-2, 1]\) is \(-4\).