Derivatives Adv Calc: Show f'(x) = f'(0)f(x)

[chief12]

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'(0)f(x)

Homework Equations

The Attempt at a Solution

f(x+0) = f(x) = f(x)f(0)
this shows f(0) = 1

then i get stuck..

 

[LCKurtz]

Homework Statement

function f is differentiable when x=0,

f'(0) is not equal to zero for all real Numbers

What does "for all real numbers" have to do with f'(0)?

f(a+b) = f(a)f(b)

show f'(x) = f'(x)f(x)

You clearly haven't stated the problem correctly since f(x) = e^x is a counterexample.

 

[chief12]

What does "for all real numbers" have to do with f'(0)?



You clearly haven't stated the problem correctly since f(x) = e^x is a counterexample.

\for some reason it quoted wrong i guess, it said f'(x) = f'(0)f(x)

 

[Dick]

Write f'(x) as a difference quotient.

 

[LCKurtz]

What happens when you try to calculate f'(x) by taking the limit of the difference quotient?

 

[chief12]

What happens when you try to calculate f'(x) by taking the limit of the difference quotient?

I don't know what that means, please explain... test tomorrow

 

[gb7nash]

Definition of the derivative via difference quotients:

http://en.wikipedia.org/wiki/Derivative

 

[LCKurtz]

What happens when you try to calculate f'(x) by taking the limit of the difference quotient?

I don't know what that means, please explain... test tomorrow

Surely the definition of a derivative is in your text:

$$f'(x) = \lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}$$