Is it possible

[Axecutioner]

Main Question or Discussion Point

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

 

[rock.freak667]

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)=e^x, then f'(x) = e^x = f(x).

 

[Axecutioner]

Oh, didn't think about that. XD I kept trying Trig to make it work....

Are there any other ways?

 

[rock.freak667]

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 e^x would satisfy the condition. I think that is the only function, that I know of anyhow.

 

[micromass]

Indeed, every function of the form $$f(x)=Ce^x$$, with $$C\in \mathbb{R}$$ will do. There are no other functions that equal it's own derivative...