Answered

Select the correct answer.

What is the average rate of change of [tex]\( f(x) \)[/tex] over the interval [tex]\([-3, 2]\)[/tex]?

[tex]\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-5 & -150 \\
\hline
-3 & -36 \\
\hline
-1 & -2 \\
\hline
0 & 0 \\
\hline
1 & 0 \\
\hline
2 & 4 \\
\hline
\end{array}
\][/tex]

A. -40
B. -8
C. 8
D. 32



Answer :

GinnyAnswer
To find the average rate of change of [tex]\( f(x) \)[/tex] over the interval [tex]\([-3, 2]\)[/tex], we will use the values of [tex]\( f(x) \)[/tex] at [tex]\( x = -3 \)[/tex] and [tex]\( x = 2 \)[/tex].

From the table, we have:
[tex]\[ f(-3) = -36 \][/tex]
[tex]\[ f(2) = 4 \][/tex]

The formula for the average rate of change of a function [tex]\( f(x) \)[/tex] over an interval [tex]\([a, b]\)[/tex] is given by:
[tex]\[ \text{Average rate of change} = \frac{f(b) - f(a)}{b - a} \][/tex]

Here, [tex]\( a = -3 \)[/tex] and [tex]\( b = 2 \)[/tex].

Substituting the values in the formula:
[tex]\[ \text{Average rate of change} = \frac{f(2) - f(-3)}{2 - (-3)} \][/tex]

Now, plug in the given values:
[tex]\[ \text{Average rate of change} = \frac{4 - (-36)}{2 - (-3)} \][/tex]

Simplify the expression by adding inside the numerator and subtracting in the denominator:
[tex]\[ \text{Average rate of change} = \frac{4 + 36}{2 + 3} \][/tex]

[tex]\[ \text{Average rate of change} = \frac{40}{5} \][/tex]

[tex]\[ \text{Average rate of change} = 8 \][/tex]

Therefore, the average rate of change of [tex]\( f(x) \)[/tex] over the interval [tex]\([-3, 2]\)[/tex] is:
[tex]\[ \boxed{8} \][/tex]
So, the correct answer is [tex]\( \text{C. 8} \)[/tex].

Other Questions