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# Rate of change [Solved!]

### 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

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

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

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

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

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

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

ok, thank u

X

ok, thank u