Question

Find the average rate of change of f ( x ) = 9 x 2 − 7 on the interval [ 2 , a ] . Your answer will be an expression involving a

Answer 1

9a + 18

Explanation:

so the first step is to evaluate the value of f(2).

`f(2) = 9(2)^2-7\\f(2)=9(4)-7\\f(2)=36-7\\f(2)=29`

Now that we have this value we can use the slope formula (y2 - y1) / (x2 - x1) where y2 is f(a), y1 is 29, x2 is a, and x1 is 2

`(f(a)-29)/(a-2)\\\\((9a^2-7)-29)/(a-2)\\(9a^2-36)/(a-2)`

Now from here we can use long division to simplify it further

`9a^2/a = 9a\\9a(a-2)=9a^2-18a\\(9a^2-36)-(9a^2-18a)\\18a-36\\\\18a/a=18\\18(a-2)=18a-36\\(18a-36)-(18a-36)\\0\\\\9a+18`