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7 Dec 2007 02:59:24 IST

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1051

How do we represent a 'double derivative' graphically?

None

Well, my question was:

If dy/dx is a slope of a tangent of a curve, then, how to represent d²y/dx²graphically?

Please explain me with a diagram.

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Comments (19)

Krishna Gopal Singh

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7 Dec 2007 03:06:03 IST

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we cannot represent d2y/dx^2 graphically but it is related to curvature of the graph.

Indzee ...

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7 Dec 2007 03:24:35 IST

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Please gimme some satisfactory reply

abc xyz

Blazing goIITian

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7 Dec 2007 07:32:23 IST

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eqn of that tangent will be in the form
dy/dx = mx + c
thus d2y/dx2 = m
which is slope of tangent.
hope its right.

pardesi .svk

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7 Dec 2007 08:50:44 IST

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no that isn't right m and c are also functions of x

abc xyz

Blazing goIITian

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7 Dec 2007 15:27:57 IST

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yeah man ur right. thanx.

Indzee ...

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7 Dec 2007 22:30:49 IST

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Then wats the actual answer!!

... plz plz .. I cannot proceed through my studies!!.. help... If we cannot represent it graphically, then plz gimmie some... reason.!!

Indzee ...

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7 Dec 2007 22:33:30 IST

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Is there no one in goiit.com who can answer my question!! Plz help.. urgent

Tarin Bansal

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7 Dec 2007 22:38:44 IST

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Let dy/dx on any curve at a given point=m.
Now d2y/dx2 is the slope of dy/dx which is m and m is constant for a given point on the curve.

Therefore, d2y/dx2 should be a straight line y=m.

Rate me if I satisfied.
Correct me if I am wrong.

abc xyz

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7 Dec 2007 22:41:20 IST

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tarin thats the mistake i made. in a graph you consider the entire axis not one point.

p karthik

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7 Dec 2007 22:44:13 IST

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hey..see iitz..lik this....d/dx of sinx is cos z...rite..d/dx(d/dx)is -sinx... it all means..lets say ..there..1 function...f(X)...d/dx represents..rate of change of y wrt x..bt the...tangents slope also varies...i.e..rate of change of(rate of change..) hope u got it..if no..plz..tell me..i can mak it even more..clear.....nd i pity u wen u say.. i cannot study..wid a dbt in mind..rem..u must learn 2 move on..co..2 get into iit..u need not no...evrything... u just need 2 hav gr8 attitude,...

Tarin Bansal

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7 Dec 2007 22:46:12 IST

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for entire curve, dy/dx itself will be variable.
May be in that case, take
y'=d2y/dx2=F(x)
F(x) is the double derivative of the curve, then simply draw the graph of y'=F(x)

Indzee ...

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7 Dec 2007 22:54:56 IST

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You mean a tangent drawn on a tangent, ie (if x=m as u say) dy/dx should be = dy2/dx2 , ... but thats not possible! coz we get two different values when we differentiate a function twice!! .. well I cannot claim that you are wrong (coz im still in 11th, n new in goiit)... but if I m wrong, then wats da actual answer???

Indzee ...

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7 Dec 2007 22:58:52 IST

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@ tarin

Sorry for the abve thing ... posted by mistake^^^

Tarin Bansal

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7 Dec 2007 23:03:49 IST

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Sorry for what?

Aatish Pandit

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7 Dec 2007 23:10:49 IST

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hey buddy where do you wanna represent d2y/dx2.......

If you are trying to plot it in X-Y plane then you may not be able to do that........

But you can do so in X-(dy/dx) plane.......as a tangent at any point in curve.........

Indzee ...

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8 Dec 2007 00:54:00 IST

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Hey dude, that was the perfect answer w.r.t. "me", rather, I could have been too idiot to ask such a stupid question.... I understood what you mean!!

What I understood???

Suppose if,

y = x³+ x²+ x + 1

Then,

dy/dx = 3x²+ 2x + 1

So,

d²x/dy²= 6x + 2 (no need to consider this in graph)

Now, look at these graphs... he he... Yeh! I got it at last ... I cannot resist my xitement!! But say me if I have mistaken somewhere... and "Rate me" coz I am the person who has answered my question perfectly (I mean with graphs) but still, the credit goes to Aatish (special thanx to him)???

Indzee ...

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8 Dec 2007 01:08:10 IST

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Look at the graphs below (graphs of the example mentioned above)... and say me whether they are right .

Indzee ...

Hot goIITian

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8 Dec 2007 01:11:53 IST

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So we have finally got the graph of a double derivative!!!

Indzee ...

Hot goIITian

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8 Dec 2007 01:12:18 IST

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Thanks to aatish

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