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Differential Calculus

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13 Sep 2007 23:48:44 IST

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higher order derivative

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what is the real physical significance(on coordinate axes) of higher order derivative that we use in maxima while deciding a max or min function.

like we know that differntiating once means finding a unique tangent but then what double differntiation stands for or more higher derivatives.

pls answer when you are fully convinced about your answer becoz my friends this can lead to misconceptions.

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Neeraj Agarwal

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Joined: 22 Jan 2007

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14 Sep 2007 12:30:14 IST

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second derivative gives the shape of graph....(which i think u know)

now i m giving a useless explanation......to clear ur doubt...
u find the first derivative.....i.e. if u replace values of x in that derivative, u get the slope of tangent at that point.so u can consider this as another function and draw its graph....

now u again find derivative...this means u r finding derivative of a new function....

if u r getting confused...then just forget the above explanation..

Mahesh Jain

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14 Sep 2007 12:33:30 IST

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well after double differentiation u get the Convex and concave shape of graph and also the point of inflexion

and more higher order derivatives for a function to plot graph has no significance

rate if u r satisfied

Enrique Iglesias

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Joined: 12 Sep 2007

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17 Sep 2007 21:36:27 IST

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second derivative tells us about the trend of the first derivative.

For example...2nd derivative of x with t tells us about how velocity is changing.

if dy/dx=0, y is at its maximum or minimum
bur if dy/dx=0 and d2y/dx2 = +ive..it is minimum ; and if d2y/dx2=-ive..it is maximum

Further..double derivative is some kind of 'infornation ahead'...if dy/dx=0 and d2y/dx2 is also equla to 0 then we can safely say that y is not only at its maximum is likely to change very slowly w.r.to x...i.e..a extended maximum kind of..

But if dy/dx=0 and d2y/dx2 is large +ive or -ive.. y is at maximum is only for ashort duration or length ...it'll chnage quickly...

[ in fact if dy/dx=0, d2y/dx2=0 and d3y/dx3 =0..we can say that it is likely to stay max or min for still longer...}...

hope it helps

rate if satisfied "

Gaurav |spideyunlimited| Ragtah

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Joined: 16 Dec 2006

Posts: 3373

20 Sep 2007 20:54:32 IST

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first order derivative tells us if the function is increasing or decreasing.
then second order derivative tells us if the graph is concave or convex shaped. if it is concave that means a minima is present nearby and if its convex means maxima is obtained

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