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Math Help - Calc BC differentiation Functin Problem

  1. #1
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    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
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  2. #2
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    Quote Originally Posted by r2d2 View Post
    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) ?
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  3. #3
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    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?
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  4. #4
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    Quote Originally Posted by r2d2 View Post
    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?
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