hello, need your help

find all function differentiable over

is differentiable over

Printable View

- April 15th 2009, 01:30 PMlinda2005Find a differentiable function with the given properties
hello, need your help

find all function differentiable over

is differentiable over - April 15th 2009, 02:06 PMCalculus26
Ok not to be a pain but the word is differentiable not derivable.

Taking the square root

f ' ^2 -f = 1 or -1

Differentiate -- in either case

2f " f ' -f ' = 0

f ' (2f"-1) = 0

Now solve f ' = 0 (use original equation to find values of c) and 2f " - 1 = 0

That should be enough to get you to the end - April 15th 2009, 02:13 PMJhevon
- April 15th 2009, 02:31 PMlinda2005
**Calculus26 it's**and not - April 15th 2009, 02:44 PMCalculus26
Sorry I read it too quickly I was seeing

[f '^2 -f]^2 = 1 for the original

For (f ')^2 - f^2 =1

the process is still the same

2f ' f "- 2 f f '= 0

f ' = 0 or f '' -f = 0

yields f = c from which there are no solutions

or f " -f = 0 which yield Acos(x) + Bsin(x) now apply f '(0) = 1

and finish - April 15th 2009, 03:09 PMCalculus26
I believe there are no solutions as f ' (0) =1 yields f =Acos(x) +sin(x)

Plugging this into the original there are no values of A Solving the equation. - April 15th 2009, 03:20 PMlinda2005
- April 15th 2009, 03:26 PMJhevon
- April 15th 2009, 03:29 PMCalculus26
Ok I've made every possible mistake on this to now--thats what i get for hurrying

we get f = Ae^t + Be^-t

f ' (0) yields A+B =1

Substituting into original equation yields -4AB =1

Now solve --solutions are when A = (2^1/2+1)/2 or (1-2^1/2)/2

with corresponding values for B = 1 -A

Sorry for the mistakes - April 15th 2009, 03:37 PMJhevon
i'm sure you can find more mistakes to make if you tried ;)

Quote:

Sorry for the mistakes

did you double check your solutions for A? :D

i'm not going to check them, i trust you (Nod) - April 15th 2009, 03:47 PMCalculus26
I rechecked for both A and B in the original both by hand and with Mathcad to make sure-- thanx for the kind words

But still I always told my students to slow down --Calculus is more about patience than intelligence I'd say--too bad I don't follow my own advice.

That's what happens a year removed from teaching--skills are slipping - April 15th 2009, 04:15 PMlinda2005
I find I'm wrong or you are Calculus26:D( f ' (0) yields A+B =1 false we have f ' (0) yields A-B =1) thanks you guys xxx

- April 15th 2009, 04:34 PMCalculus26
Damn--- you're right using the initial condition A - B = 1 not A+B =1

as I said before--my solution satisfies the equation which is where I checked my results but not the initial conditions.

Now I quit

3 mistakes on one problem - April 15th 2009, 04:50 PMCalculus26
By the way not that it matters that much but

http://www.mathhelpforum.com/math-he...5c0cddb6-1.gif is also known as the hyperbolic sine and written

http://www.mathhelpforum.com/math-he...5c0cddb6-1.gif = sinh(x)

You may see the answer written that way

Thanx for your kindness amongst my blunders I should have stopped after

describing the process. - April 15th 2009, 04:54 PMJhevon
i told you you could find more mistakes if you tried :D

that was mean. i am only messing with you**Calc**. but yes, if you find you made 2 blunders, just resort to describing the process and letting the OP do the groundwork. this comes with experience on forums (Nod)

take care (Handshake)