Questions: What is the average rate of change of g over the interval -3 ≤ t ≤ 1? Give an exact number.

Transcript text: What is the average rate of change of $g$ over the interval $-3 \leq t \leq 1$ ? Give an exact number.

Solution

Solution Steps

To find the average rate of change of a function $ g $ over an interval $[-3, 1]$, we use the formula for the average rate of change, which is $\frac{g(b) - g(a)}{b - a}$, where $a$ and $b$ are the endpoints of the interval. Here, $a = -3$ and $b = 1$. We need to find the values of $g(-3)$ and $g(1)$ from the given table and then apply the formula.

Step 1: Identify the Interval Endpoints

We are given the interval $[-3, 1]$. The endpoints are $a = -3$ and $b = 1$.

Step 2: Find the Function Values at the Endpoints

From the given data points:

$g(-3) = 6$
$g(1) = 0$

Step 3: Apply the Average Rate of Change Formula

The average rate of change of a function $g$ over the interval $[a, b]$ is given by: \[ \frac{g(b) - g(a)}{b - a} \] Substituting the values: \[ \frac{g(1) - g(-3)}{1 - (-3)} = \frac{0 - 6}{1 + 3} = \frac{-6}{4} = -1.5 \]