The problem involves a differentiable function f at x=0, with the condition that f'(0) is not equal to zero for all real numbers. The goal is to show that f'(x) = f'(0)f(x) given the functional equation f(a+b) = f(a)f(b).
The discussion is ongoing, with participants exploring various interpretations of the problem and raising questions about the definitions and implications of the derivative. Some guidance has been offered regarding the definition of the derivative, but there is no explicit consensus on the problem's formulation or approach.
There are indications of confusion regarding the problem statement and its implications, as well as a mention of an upcoming test, which may influence participants' engagement and understanding.
chief12 said:Homework Statement
function f is differentiable when x=0,
f'(0) is not equal to zero for all real Numbers
f(a+b) = f(a)f(b)
show f'(x) = f'(x)f(x)
\for some reason it quoted wrong i guess, it said f'(x) = f'(0)f(x)LCKurtz said:What does "for all real numbers" have to do with f'(0)?
You clearly haven't stated the problem correctly since f(x) = ex is a counterexample.
LCKurtz said:What happens when you try to calculate f'(x) by taking the limit of the difference quotient?
LCKurtz said:What happens when you try to calculate f'(x) by taking the limit of the difference quotient?
chief12 said:I don't know what that means, please explain... test tomorrow