Is it possible...


by Axecutioner
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Axecutioner
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#1
Jan11-11, 02:31 PM
P: 32
Is it possible for f(x) to be equal to f '(x)? I've been trying all day to make it work and have gotten nothing.

Thanks
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rock.freak667
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#2
Jan11-11, 02:39 PM
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Quote Quote by Axecutioner View Post
Is it possible for f(x) to be equal to f '(x)? I've been trying all day to make it work and have gotten nothing.

Thanks
Sure, if f(x)=ex, then f'(x) = ex = f(x).
Axecutioner
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#3
Jan11-11, 02:41 PM
P: 32
Oh, didn't think about that. XD I kept trying Trig to make it work....

Are there any other ways?

rock.freak667
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#4
Jan11-11, 02:52 PM
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Is it possible...


Quote Quote by Axecutioner View Post
Oh, didn't think about that. XD I kept trying Trig to make it work....

Are there any other ways?
if you solve the differential equation

f'(x)=f(x)

You'd see that any multiply of ex would satisfy the condition. I think that is the only function, that I know of anyhow.
micromass
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#5
Jan11-11, 05:11 PM
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Indeed, every function of the form [tex]f(x)=Ce^x[/tex], with [tex]C\in \mathbb{R}[/tex] will do. There are no other functions that equal it's own derivative...


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