MHB Average rate of change in the function from x1 to x2

[Taryn1]

So this is my first question here, and I hope I'm doing it right!

My question is basically this:

Find the average rate of change of the function from x1 to x2.

f(x) = x^2 + 12x -4

I'm also new to precalc, so please don't blame me if this is a really easy question! It doesn't seem to make sense to me, I think I overthink stuff sometimes. Do I just pick two x-values and then find the difference between the results?

(x^2 means x to the power of 2 or x squared)

 

[Taryn1]

Oh my gosh...title typo. Meant average, obviously.

 

[Jameson]

So this is my first question here, and I hope I'm doing it right!

My question is basically this:

Find the average rate of change of the function from x1 to x2.

f(x) = x^2 + 12x -4

I'm also new to precalc, so please don't blame me if this is a really easy question! It doesn't seem to make sense to me, I think I overthink stuff sometimes. Do I just pick two x-values and then find the difference between the results?

(x^2 means x to the power of 2 or x squared)

Hi Taryn, (Wave)

Welcome to MHB! I fixed the title for you. No worries - typos happen!

Ok so in general to find the average rate of change between two points, $a$ and $b$, we use:
$$\text{Average change = } \frac{f(b)-f(a)}{b-a}$$

So you were only asked about the general variables, $x_1$ and $x_2$? Were these given any particular values?

 

[Taryn1]

Yeah, it was only the general variables x1 and x2, no particular values. So I just make up my own?

And thanks for the help!

 

[Jameson]

Yeah, it was only the general variables x1 and x2, no particular values. So I just make up my own?

And thanks for the help!

I would leave it in general terms of $x_1$ and $x_2$ then. What do you get when you plug in the following?
$$\frac{f(x_2)-f(x_1)}{x_2-x_1}$$

 

[Taryn1]

Wow, I just realized I had made a super dumb mistake! Thanks for your help, Jameson. I've got it now - they gave me values for {x}_{1} and {x}_{2}. lol!