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Find G'(1) and F'(2)

  1. Nov 30, 2011 #1
    1. The problem statement, all variables and given/known data

    Let f and g be the functions in the table below.

    x f(x) g(x) f'(x) g'(x)
    1 3 2 4 6
    2 1 3 5 7
    3 2 1 7 9

    2. Relevant equations

    If F(x) = f(f(x)), find F '(2).
    If G(x) = g(g(x)), find G'(1).

    3. The attempt at a solution

    i took F(x)=f(f(x)) meaning when f(x)=3, F(x)= 3(3)=9
    and
    G(x)=g(g(x)) to mean when g(x)=2 G(x)=2(2)=4

    so if i am looking at this correctly, can someone help me on where to go from here. please
     
  2. jcsd
  3. Nov 30, 2011 #2

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    No, that's not what it means. f(f(x)) means evaluate f(x), then evaluate f(x) at that point. So for example:

    f(f(1))=f(3)=2
    g(g(1))=g(2)=3
     
  4. Nov 30, 2011 #3

    Mark44

    Staff: Mentor

    You need to work on understanding function notation better. From the table f(1) = 3, f(2) = 1, and f(3) = 2.

    There is no formula for f(x), so it's meaningless to say that f(x) = 3.

    This problem is all about understanding the chain rule. You also need to understand the difference between F'(x) and F'(2).

    First, find an expression for F'(x).
    Next, evaluate F'(x) at x = 2.

    The other problem is exactly the same.
     
  5. Nov 30, 2011 #4
    F'(x)=f'(f(x))
    G'(x)=g'(g(x))
    ??
     
  6. Dec 1, 2011 #5

    Mark44

    Staff: Mentor

    That's a start, but you're missing a factor that comes from the chain rule.
     
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