Is it possible

  • #1

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
 

Answers and Replies

  • #2
rock.freak667
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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).
 
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  • #3
Oh, didn't think about that. XD I kept trying Trig to make it work....

Are there any other ways?
 
  • #4
rock.freak667
Homework Helper
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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.
 
  • #5
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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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