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Homework Help: Evaluating functions

  1. Oct 4, 2004 #1
    if
    L(x)=sqrt(x)*f(x)
    f(9)=3
    F'(9)=(-4)

    find L'(9)

    I think I need to use the product rule:

    L'(9)=0.5x^(-0.5)*f(x)+f'(x)*sqrt(x)
    L'(9)=(1/6)*3+(-4)*3
    L'(9)=-11.5

    Also, what if the question asked for f^3(x), how would I set that up?
     
  2. jcsd
  3. Oct 4, 2004 #2
    More generally if I let f(x) and g(x) denote two functions then the first derivative of their product, viz. g(x)f(x) is written as

    [tex]\frac{d[gf]}{dx} = g(x)\frac{df}{dx} + f(x)\frac{dg}{dx}[/tex]

    you seem to have applied the product rule correctly. I believe you mean f'(3) or f(x)^3. Is it so?

    You know that f(x = 9) = 3 and f'(x = 9) = -4. Do you think this information is sufficient to fix f'(x = 3) or f(x = 3)?
     
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