# Thread: Calc BC differentiation Functin Problem

1. ## Calc BC differentiation Functin Problem

Let $\displaystyle f$ be differentiable functions with the following properties:

I. $\displaystyle g(x) > 0 for all x$
II. $\displaystyle f(0) = 1$

If $\displaystyle h(x)= f(x)g(x) and h'(x)= f(x)g'(x), then f(x)= ?$

A. f'(x)
B. 0
C. 1
d. g(x)

I am confused about where to begin this problem. Any ideas?

Thanks

2. Originally Posted by r2d2
Let $\displaystyle f$ be differentiable functions with the following properties:

I. $\displaystyle g(x) > 0 for all x$
II. $\displaystyle f(0) = 1$

If $\displaystyle h(x)= f(x)g(x) and h'(x)= f(x)g'(x), then f(x)= ?$

A. f'(x)
B. 0
C. 1
d. g(x)

I am confused about where to begin this problem. Any ideas?

Thanks
h'(x) = f(x)g'(x) + g(x)f'(x) = f(x)g'(x)

what does that say about the product g(x)f'(x) ?

further, since g(x) > 0 foa all x, what does that say about f'(x) ?

finally, what does that say about f(x) ?

3. so if g(x)f'(x) = 0, and where g(x) cannot be 0, then than means f(x) must be a constant, so the answer would be 1. Would that be correct?

4. Originally Posted by r2d2
so if g(x)f'(x) = 0, and where g(x) cannot be 0, then than means f(x) must be a constant, so the answer would be 1. Would that be correct?