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Math Help - Values for the function f(x) and f'(x)

  1. #1
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    Values for the function f(x) and f'(x)

    hey did i set these problems up right? as well what do they mean when they have:

    g'(2), where g(x)= f(f(x))

    along with the h'(2) and k'(x)

    thx
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by cyberdx16 View Post
    hey did i set these problems up right? as well what do they mean when they have:

    g'(2), where g(x)= f(f(x))

    along with the h'(2) and k'(x)

    thx
    For starters they are looking for numerical answers, if the information is there to provide them. Let me do the first one as an example:

    f(f(x)+1) at x = 2.

    This is f(f(2)+1) = f(3+1) according to the chart
    f(3+1) = f(4) = 5 again, according to the chart.

    -Dan
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  3. #3
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    yes i know that, but what i did was set them up as dy/dx and then i can plug in the # values. i was just wondering if they were set up right in the terms of f(x)
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  4. #4
    Forum Admin topsquark's Avatar
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    a) Unless part of the problem has been cut off you didn't need to take a derivative. Just plug in the values as I showed you.

    d) y = f(x^2-3)
    y' = f'(x^2-3)*2x

    e) k(x) = f(x^2)/f(x)
    Use the quotient rule:
    k'(x) = [f'(x^2)*2x*f(x) - f(x^2)*f'(x)]/[f(x)]^2

    The others look fine.

    I noted that most of the mistakes are due to an improper application of the composition rule:
    y = f(g(x)) => y' = f'(g(x))*g'(x)

    Make sure when you take the derivative of the "outer" function, f, you keep the same argument g(x) as you had in the original part of the problem.

    -Dan
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  5. #5
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    cool thx a bunch
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  6. #6
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    so what do they g'(2)??? cuz in the directions it says i am able to write unknown if not enough info is given... so would g'(2) be a time were not info available?

    EDIT: i think i got it duh! it rep what x is right?
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by cyberdx16 View Post
    so what do they g'(2)??? cuz in the directions it says i am able to write unknown if not enough info is given... so would g'(2) be a time were not info available?

    EDIT: i think i got it duh! it rep what x is right?
    Yup!

    -Dan
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