Find the average rate of change of $$ g(x)=2 x+8 $$ from $$ x=6 $$ to $$ x=10 $$. Simplify your answer as much as possible.

Question

UpStudy AI · Accepted Answer

To find the average rate of change of the function $$ g(x) = 2x + 8 $$ from $$ x = 6 $$ to $$ x = 10 $$, you can use the following formula:

$$
\text{Average rate of change} = \frac{g(b) - g(a)}{b - a}
$$

where $$ a = 6 $$ and $$ b = 10 $$.

1. **Calculate $$ g(10) $$:**
$$
g(10) = 2(10) + 8 = 20 + 8 = 28
$$

2. **Calculate $$ g(6) $$:**
$$
g(6) = 2(6) + 8 = 12 + 8 = 20
$$

3. **Compute the average rate of change:**
$$
\text{Average rate of change} = \frac{28 - 20}{10 - 6} = \frac{8}{4} = 2
$$

**Answer:** The average rate of change is $$ 2 $$.
The average rate of change is 2.

Find the average rate of change of \( g(x)=2 x+8 \) from \( x=6 \) to \( x=10 \). Simplify your answer as much as possible.