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Problem 1

# Calculate the average rate of change of the given function over the given interval. Where appropriate, specify the units of measurement. HINT [See Example 1.] $$\begin{array}{|c|c|c|c|c|} \hline \boldsymbol{x} & 0 & 1 & 2 & 3 \\ \hline \boldsymbol{f ( x )} & 3 & 5 & 2 & -1 \\ \hline \end{array}$$ Interval: $$[1,3]$$

Expert verified
The average rate of change of the function over the interval $$[1,3]$$ is $$-3$$. Units of measurement are not specified.
See the step by step solution

## Step 1: Identify the endpoints of the interval

The given interval is $$[1,3]$$. This means we are asked to find the average rate of change of the function from $$x = 1$$ to $$x = 3$$.

## Step 2: Find the function values at the endpoints of the interval

First, we need to find the function values at the endpoints of the interval. From the table, we have: $$f(1) = 5$$ and $$f(3) = -1$$

## Step 3: Calculate the average rate of change of the function

To calculate the average rate of change of the function on the interval $$[1,3]$$, we will use the formula: Average rate of change $$=\dfrac{f(3) - f(1)}{3-1}$$ Now substitute the function values found in Step 2, and we have: Average rate of change $$=\dfrac{-1 - 5}{3-1} = \dfrac{-6}{2} = -3$$ The average rate of change of the function over the interval $$[1,3]$$ is $$-3$$. In this case, the units of measurement are not specified.

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