Question

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

14
Start Fraction 1 over 4 End Fraction

16
16

4
4

−4

Answer 1

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

First, we need to find \( f(-3) \) and \( f(5) \):

1. Calculate \( f(-3) \):
\[
f(-3) = 2(-3)^2 - 6 = 2(9) - 6 = 18 - 6 = 12
\]

2. Calculate \( f(5) \):
\[
f(5) = 2(5)^2 - 6 = 2(25) - 6 = 50 - 6 = 44
\]

Now, substituting \( f(-3) \) and \( f(5) \) 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

\[
\boxed{4}
\]