Questions: Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval (2 leq x leq 3). (x) (f(x)) 2 28 3 19 4 12 5 7

Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval (2 leq x leq 3).

(x) (f(x))

2 28

3 19

4 12

5 7

Transcript text: Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval $2 \leq x \leq 3$. \begin{tabular}{|c|c|} \hline$x$ & $f(x)$ \\ \hline 2 & 28 \\ \hline 3 & 19 \\ \hline 4 & 12 \\ \hline 5 & 7 \\ \hline \end{tabular}

Solution

Solution Steps

Step 1: Identify the values of f(a) and f(b)

Located the values of the function at the endpoints of the interval: f(a) = 28, f(b) = 19.

Step 2: Calculate the difference in function values

The difference in function values is calculated as: f(b) - f(a) = 19 - 28 = -9.

Step 3: Calculate the difference in x values

The difference in x values is calculated as: b - a = 3 - 2 = 1.

Step 4: Compute the average rate of change

The average rate of change is calculated using the formula: \(\frac{f(b) - f(a)}{b - a}\) = \(\frac{-9}{1}\) = -9.

Final Answer:

The average rate of change of the function over the interval [2, 3] is -9.

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