Question

Calculate the average rate of change for f(x) = 5x + 3 from x = 8 to x = 8 + h.

Answer 1

The average rate of change is given by

`A(x)=(f(b)-f(a))/(b-a)`

Here a=8 and b=8+h

`\begin{gathered} f(x)=5x+3 \\ f(8)=5*8+3=43 \\ f(8+h)=5(8+h)+3 \\ \text{ =40+5h+3} \\ \text{ =43+5h} \end{gathered}`

Thus,

`A(x)=(43+5h-43)/(8+h-8)=(5h)/(h)=5`

Thus the average rate is 5.