text: # Calc BC differentiation Functin Problem
  
  • Oct 21st 2009, 12:51 PM
  r2d2
  Calc BC differentiation Functin Problem
  Let $f$ be differentiable functions with the following properties:
  
  I. $g(x) > 0 for all x$
  II. $f(0) = 1$
  
  If $h(x)= f(x)g(x) and h'(x)= f(x)g'(x), then f(x)= ?$
  
  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 $f$ be differentiable functions with the following properties:
  
  I. $g(x) > 0 for all x$
  II. $f(0) = 1$
  
  If $h(x)= f(x)g(x) and h'(x)= f(x)g'(x), then f(x)= ?$
  
  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)
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