Average rate of change in the function from x1 to x2

In summary, to find the average rate of change of the function between two points, $a$ and $b$, you use:$$\text{Average change = } \frac{f(b)-f(a)}{b-a}$$
  • #1
Taryn1
25
0
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)
 
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  • #2
Oh my gosh...title typo. Meant average, obviously.
 
  • #3
Taryn said:
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?
 
  • #4
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!
 
  • #5
Taryn said:
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?
$$\frac{f(x_2)-f(x_1)}{x_2-x_1}$$
 
  • #6
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!
 

FAQ: Average rate of change in the function from x1 to x2

What does the average rate of change in a function from x1 to x2 represent?

The average rate of change in a function from x1 to x2 represents the average amount of change in the output of the function over a specific interval of the input. It is calculated by finding the slope of the line connecting the two points (x1, f(x1)) and (x2, f(x2)) on the graph of the function.

How is the average rate of change in a function from x1 to x2 calculated?

The average rate of change is calculated by finding the difference in the output values (f(x2) - f(x1)) and dividing it by the difference in the input values (x2 - x1). This can also be expressed as (f(x2) - f(x1)) / (x2 - x1).

What is the difference between average rate of change and instantaneous rate of change?

The average rate of change is calculated over a specific interval of the input, while the instantaneous rate of change is calculated at a specific point on the graph of the function. The average rate of change gives an overall view of the function's behavior, while the instantaneous rate of change provides information about the function's behavior at a specific point.

How can the average rate of change be used to predict future values of a function?

If the average rate of change of a function is constant over a specific interval, it can be used to predict future values of the function. This is based on the assumption that the function will continue to behave in a similar manner over that interval.

What does a negative average rate of change indicate?

A negative average rate of change indicates that the function is decreasing over the given interval. This means that as the input increases, the output decreases.

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