# Thread: Average rate of change on the inteval

1. ## Average rate of change on the inteval

Hello, I've managed to solve (at least I think) the following problem:

Find the average rate of change of f(x) = 2x2 -x + 1 on the interval [3, 3+h].

Though I solved it in 2 different ways and ended up with 2 different answers. My answers were -7 or -11 + 2h. I'm not sure which is the right answer or if neither is right. I'm positive I managed to set up the formula correctly, which I showed below:

F(x) = (2(3+h)2 - (3+h) + 1 - 16)/3+h-3

Any help is appreciated, and if you provide an explanation I would be even more thankful.

2. ## Re: Average rate of change on the inteval

$\dfrac{f(3+h) - f(3)}{(3+h)-3}$

$\dfrac{2(3+h)^2 - (3+h) + 1 - [2(3)^2 - 3 + 1]}{h}$

$\dfrac{2(9+6h+h^2) - 3 - h + 1 - 16}{h}$

$\dfrac{18 + 12h + 2h^2 - 3 - h + 1 - 16}{h}$

now ... combine like terms in the numerator & finish it.

you should get $11 + 2h$

3. ## Re: Average rate of change on the inteval

Originally Posted by reina
Hello, I've managed to solve (at least I think) the following problem:

Find the average rate of change of f(x) = 2x2 -x + 1 on the interval [3, 3+h].

Though I solved it in 2 different ways and ended up with 2 different answers. My answers were -7 or -11 + 2h. I'm not sure which is the right answer or if neither is right. I'm positive I managed to set up the formula correctly, which I showed below:

F(x) = (2(3+h)2 - (3+h) + 1 - 16)/3+h-3

Any help is appreciated, and if you provide an explanation I would be even more thankful.
It's good that you showed where you started, but it does not help us figure out where you went wrong in the working.

Except for a missing pair of parentheses in the denominator of the difference quotient, your set up was correct.

4. ## Re: Average rate of change on the inteval

You say "I solved it in 2 different ways and ended up with 2 different answers". What were those two different ways?