Question

Find the average rate of change for f(x) = x2 + 9 from x = 4 to x = 7.

Answer 1

We can find the average rate of change with the following formula

`(f(b)-f(a))/(b-a)`

Which is defined inside the interval

`a\leq x\leq b`

In other words, this formula allows us to calculate the average rate of change inside the interval [a,b], which in this case is [4,7].

First, we find f(a) and f(b):

`\begin{gathered} f(4)=4^2+9=16+9=25 \\ f(5)=5^2+9=25+9=34 \end{gathered}`

Now, we use the formula

`(34-25)/(7-4)=(9)/(3)=3`

Therefore, the average rate of change of f(x) from x=4 to x=7 is 3.