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How derivatives used to find out rates of change?
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How derivatives used to find out rates of change?
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Wasee
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How derivatives used to find out rates of change?
«
on:
12/01/2009 08:41:43 »
Wasee asked the Naked Scientists:
Hello,
I know what derivatives are and how to find the derivative of a function, but what bothers me is how they are used to find out rates of change velocity, accelaration etc
Thanks
What do you think?
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Chemistry4me
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How derivatives used to find out rates of change?
«
Reply #1 on:
12/01/2009 09:34:56 »
distance (differentiate) > velocity (differentiate) > acceleration
Draw the graph and then its derivative and you'll see it as the gradient function. The x-intercepts of the gradient function are the turning point(s) of the original graph.
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Chemistry4me
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How derivatives used to find out rates of change?
«
Reply #2 on:
12/01/2009 10:14:11 »
If I was to draw a diagram, like so:
[diagram=391_0]
The co-ordinates of P are (x, (
f
(x)). If the x-coordinate of Q is (x+h) then the y-coordinate of Q is
f
(x+h). Gradient of PQ = QR/PR
= (
f
(x+h) -
f
(x))/h
As Q 'slides down' the curve: In the limit, as Q→P, and h→0, the gradient of the chord PQ approaches the gradient of the tangent at point P.
Gradient of the tangent at P = lim(h→0) (
f
(x+h)-
f
(x))/h
This is often referred to as the gradient function written
f
'(x)
i.e
f
'(x) = lim(h→0) (
f
(x+h)-
f
(x))/h
This limit is used when calculating the derivative of
f
(x) from first principles. The derivative
f
'(x) is interpreted as the rate of change of y with respect to x. Hope you understood that [
]
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lyner
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How derivatives used to find out rates of change?
«
Reply #3 on:
12/01/2009 12:09:13 »
Mr Worthington told us that in 1961!!!
And it hasn't changed.
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Chemistry4me
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How derivatives used to find out rates of change?
«
Reply #4 on:
12/01/2009 22:41:30 »
Quote from: sophiecentaur on 12/01/2009 12:09:13
Mr Worthington told us that in 1961!!!
I presume that was your maths teacher.
Am I correct (with the calculus bit)?
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lyner
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How derivatives used to find out rates of change?
«
Reply #5 on:
12/01/2009 23:00:20 »
A legend!!
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How derivatives used to find out rates of change?
«
Reply #5 on:
12/01/2009 23:00:20 »
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