Question

Find the average rate of change of k(x) = 4x + 11 over the interval [-19, -17].

Answer 1

Step 1:

Concept:

Use the rate of change formula below.

`\begin{gathered} \text{Rate of change = }\frac{k(b)\text{ - k(a)}}{b\text{ - a}} \\ k(x)\text{ = 4x + 11} \\ a\text{ = -19} \\ b\text{ = -17} \end{gathered}`

Step 2

Find k(a) and k(b)

`\begin{gathered} k(-19)\text{ = 4(-19) + 11 = -76 + 11 = -65} \\ k(-17)\text{ = 4(-17) + 11 = -68 + 11= - 57} \end{gathered}`

Step 3:

`\begin{gathered} \text{Rate of change = }\frac{-57\text{ - (-65)}}{-17\text{ - (-19)}} \\ =\text{ }\frac{-57\text{ + 65}}{-17\text{ + 19}} \\ =\text{ }(8)/(2) \\ =\text{ 4} \end{gathered}`