[thechat] Tangent with a Curve

Lachlan Cannon luminosity at members.evolt.org
Tue May 7 19:38:01 CDT 2002


s t e f said:
> <who="Syed Zeeshan Haider" when="05:04 06/05/02 +0500">
>>Hi Lachlan,
>>I think, I am not proving myself a good student of Maths. Please give
>>me some example for the explanation that you gave. Let I have a point
>>(5,7) on a curve, then how I am supposed to draw a tangent on this
>>point.
>
> You're supposed to calculate the derivative at this point, aren't you?
> It gives you what we in french call the "directing coefficient" which
> is the angle of the tangent on this given point.
>
> Don't ask me for more than that, I've got a hangover and maths are
> wayyyyyyyy behind me, a long long time ago.

Hmm, well. Let's say you have a curve whose equation is y = x^3 -3x^2 + 5x
and you want the tangent line equation where x=2. First we need the
gradient of the line at that point.

dy/dx = 3x^2 - 6x + 5
when x = 2, dy/dx = 12 - 12 + 5 = 5

Now you take the equation of a line and sub the gradient in.
y = 5x + c.
Now when x =2, y = 8 - 12 + 10 = 6 So to find the value of c you sub this
co ord in.
y = 5x + c
6 = 5*2 + c
c = 6 - 10 = -4.

So the equation of the tangent line at x = 2 is y = 5x -4

Is that explained well enough?

Lach





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