# Rate of change [Solved!]

**Rismiya** 18 Dec 2015, 09:58

### My question

Write down the rate of change of the function

f (x) = x2 between x=1, and -2, 7/2, -1/2

### Relevant page

4. Derivative as an Instantaneous Rate of Change

### What I've done so far

Read examples on the page, but couldn't follow them.

X

Write down the rate of change of the function
f (x) = x2 between x=1, and -2, 7/2, -1/2

Relevant page
<a href="/differentiation/4-derivative-instantaneous-rate-change.php">4. Derivative as an Instantaneous Rate of Change</a>
What I've done so far
Read examples on the page, but couldn't follow them.

## Re: Rate of change

**Murray** 19 Dec 2015, 10:53

Hello Rismiya

The rate of change of a function at `x` is given by `dy/dx`.

Is your function actually `f(x) = x^2`?

If so, what is `dy/dx`?

It's not really possible to talk about the rate of change "between" 2 values - it changes for all values of `x`.

X

Hello Rismiya
The rate of change of a function at `x` is given by `dy/dx`.
Is your function actually `f(x) = x^2`?
If so, what is `dy/dx`?
It's not really possible to talk about the rate of change "between" 2 values - it changes for all values of `x`.

## Re: Rate of change

**Rismiya** 20 Dec 2015, 10:43

`dy/dx = 2x`

How do we find the rate of change between 1 and -2?

X

`dy/dx = 2x`
How do we find the rate of change between 1 and -2?

## Re: Rate of change

**Murray** 21 Dec 2015, 06:30

That's correct.

As I mentioned, we don't find the rate "between" 2 `x`-values (well, we can, biut we don't normally).

We need to find the rate **at** those values, by substituting.

X

That's correct.
As I mentioned, we don't find the rate "between" 2 `x`-values (well, we can, biut we don't normally).
We need to find the rate <b>at</b> those values, by substituting.

## Re: Rate of change

**Rismiya** 21 Dec 2015, 21:08

At `x = 1`, the rate of change is `2`

If `x = -2`, the rate of change is `-4`

If `x = 7/2`, the rate of change is `7`

If `x = -1/2`, the rate of change is `-1`

But what does this mean?

X

At `x = 1`, the rate of change is `2`
If `x = -2`, the rate of change is `-4`
If `x = 7/2`, the rate of change is `7`
If `x = -1/2`, the rate of change is `-1`
But what does this mean?

## Re: Rate of change

**Murray** 22 Dec 2015, 10:04

Have a look at the diagram of the parabola on this page:

Differentiation

It shows the slope at various points on the curve (i.e. values of `x`).

You have just done a similar thing - found the slope at various points around your parabola.

Hope it makes sense.

X

Have a look at the diagram of the parabola on this page:
<a href="/differentiation/differentiation-intro.php">Differentiation</a>
It shows the slope at various points on the curve (i.e. values of `x`).
You have just done a similar thing - found the slope at various points around your parabola.
Hope it makes sense.

## Re: Rate of change

**Rismiya** 23 Dec 2015, 07:37

ok, thank u

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