Question

Find the average rate of change of f(x)=6x²−3 on the interval [2,a]. Your answer will be an expression involving a

What I did so far:

I found f(2) which is 21 and that would make the function (2,21)

Then, I found f(a) which is 6a^2-3 and that would make the function (a,6a^2-3)

Answer 1

f(2) = 21 , you had that
f(a) = 6a^2 - 3

all you had to do is find the average rate of change, or more commonly known as the slope

average rate of change = (6a^2 - 3 - 21)/(a - 2)
= (6a^2 - 24)/(a-2)
= 6(a^2 - 4)/(a-2)
= 6(a+2)(a-2)/(a-2)
= 6(a+2) , a ≠ 2