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.

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`.

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.

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?

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.