Rismiya 18 Dec 2015, 09:58
Write down the rate of change of the function
f (x) = x2 between x=1, and -2, 7/2, -1/2
4. Derivative as an Instantaneous Rate of Change
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.
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`.
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?
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.
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?
Murray 22 Dec 2015, 10:04
Have a look at the diagram of the parabola on this page:
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.
X
ok, thank u