Math Is Fun Forum

juantheron

Member

Registered: 2011-10-19

Posts: 312

double derivative

what is the meaning od double derivative

and how can we say that if double derivative is > 0. Then function is Concave up

and if double derivative is < 0. Then function is Concave Down

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: double derivative

hi juan

the double derivative (used more often as the second derivative) is the first derivative of the first derivative of a function,e.g:

if f(x)=x^3 then

f'(x)=3x^2 and the

f''(x)= (f'(x))'=(3x^2)'=6x <-------this is the second (double) derivative of f(x).

thus,the second derivative is the rate of change of the first derivative.and the first is as you know the rate of change of the original function,so the larger the second derivative the faster the rate of change goes up.and since the rate of change is getting larger,the function will concave up.

what i just wrote is probably very confusing,but it was the only way i could understand it.if this is not clear then maybe you should better get an answer from other guys as well.

Last edited by anonimnystefy (2012-01-14 01:55:04)

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“Here lies the reader who will never open this book. He is forever dead.
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bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: double derivative

Hi all;

The second derivative in kinematics is called acceleration.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

juantheron

Member

Registered: 2011-10-19

Posts: 312

Re: double derivative

Thanks like we have f(x) = x^2

Then f(x) is what type of function means  concave up function or concave down function

Last edited by juantheron (2012-01-14 02:48:09)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: double derivative

Hi juan;

This will help you get a geometric feeling for it.

http://www.google.com/search?q=concave+ … 00&bih=464

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

juantheron

Member

Registered: 2011-10-19

Posts: 312

Re: double derivative

Thanks bobbym

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: double derivative

For f(x)=x^2 the 2nd derivative is positive.
The second derivative being positive implies that the graph is concave up

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.