Question

Given f(x)= 1/x+6, find the average rate of change of f(x) on the interval [8,8+h]. Your answer will be an expression involving h

Answer 1

Function:

`f(x)=(1)/(x+6)`

Interval: [ 8, 8+h ]

Average rate of change:

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

where a = 8 and b = 8 + h...

`\begin{gathered} f(b)=(1)/(b+6) \\ f(8+h)=(1)/(8+h+6)=(1)/(h+14) \\ f(8+h)=(1)/(h+14) \end{gathered}`
`\begin{gathered} f(a)=(1)/(a+6) \\ f(8)=(1)/(8+6)=(1)/(14) \end{gathered}`

Then:

`\begin{gathered} A(x)=((1)/(h+14)-(1)/(14))/(8+h-8)=((1)/(h+14)-(1)/(14))/(h)=-(1)/(14\cdot(h+14)) \\ A(x)=-(1)/(14h+196) \end{gathered}`