### Home > A2C > Chapter 14 > Lesson 14.9.1.3 > Problem9-42

9-42.

Complete the following.

1. What is the average rate of change of the function $g\left(x\right) = 6 − 2x$ over the interval $[2, 6]$?

$\frac{g(6) - g(2)}{6-2}$

2. Over the interval $[5, 7]$?

$\frac{g(7) - g(5)}{7-5}$

3. Do you think it is true that $g\left(x\right)$ will have a constant average rate of change over any interval? Why or why not?

Yes, because it is linear.

4. Prove your answer to part (c) by computing the average rate of change for $g\left(x\right)$ over the interval $[a, b]$.

$\frac{g(b) - g(a)}{b-a} = \frac{6 - 2b - (6 - 2a)}{b - a} =$