Question

(1 point)
Responses
Given the function f(x) = x^2 + 4x - 2, determine the average rate of change of the function over the interval -8 < x < 3
1
1

-1
-1

-3
-3

3

Answer 1

To find the average rate of change of the function \( f(x) = x^2 + 4x - 2 \) over the interval \( -8 < x < 3 \), we can use the formula for the average rate of change:

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

where \( a = -8 \) and \( b = 3 \).

First, we need to calculate \( f(-8) \) and \( f(3) \).

**Calculate \( f(-8) \):**
\[
f(-8) = (-8)^2 + 4(-8) - 2 = 64 - 32 - 2 = 30
\]

**Calculate \( f(3) \):**
\[
f(3) = (3)^2 + 4(3) - 2 = 9 + 12 - 2 = 19
\]

Now, we substitute these values into the average rate of change formula:
\[
\text{Average Rate of Change} = \frac{f(3) - f(-8)}{3 - (-8)} = \frac{19 - 30}{3 + 8} = \frac{-11}{11} = -1
\]

Thus, the average rate of change of the function over the interval \( -8 < x < 3 \) is \( \boxed{-1} \).