# Calc BC differentiation Functin Problem

• Oct 21st 2009, 12:51 PM
r2d2
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
• Oct 21st 2009, 01:48 PM
skeeter
Quote:

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) ?
• Oct 21st 2009, 01:55 PM
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?
• Oct 21st 2009, 02:51 PM
Jester
Quote:

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?

(Clapping)