f(x)=f'(x) for all x in R
S.T there exists a c in R such that f(x) = c exp(x) for all x
The Attempt at a Solution
By defining g = f/c, I was able to show that c= f(0)
But i am also supposed to show that c Not equal to any other value
I tried assuming that c=f(1) and cannot find a contradiction unless I plug it into f(1)=f(1).exp(1).
I am supposed to use Mean value Thm to show the contradiction. How do I go about doing it?