Question

Calculate the average rate of change over the interval [−3,5]
given the function f(x)=2x2−6
.(1 point)
Responses

14
1 fourth - no response given

16
16 - no response given

−4
negative 4 - incorrect

4

Answer 1

To calculate the average rate of change of the function \( f(x) = 2x^2 - 6 \) over the interval \([-3, 5]\), we will 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 \( b = 5 \).

1. First, we evaluate \( f(-3) \):
\[
f(-3) = 2(-3)^2 - 6 = 2(9) - 6 = 18 - 6 = 12
\]

2. Next, we evaluate \( f(5) \):
\[
f(5) = 2(5)^2 - 6 = 2(25) - 6 = 50 - 6 = 44
\]

3. Now, we can substitute these values into the average rate of change formula:
\[
\text{Average Rate of Change} = \frac{f(5) - f(-3)}{5 - (-3)} = \frac{44 - 12}{5 + 3} = \frac{32}{8} = 4
\]

Thus, the average rate of change over the interval \([-3, 5]\) is \(\boxed{4}\).