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Math Help - Say What?

  1. #1
    No one in Particular VonNemo19's Avatar
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    Say What?

    Suppose that f and g are functions such that:

    f(2)=-1, f'(2)=4, f''(2)=-2, g(2)=-3, g'(2)=2, g''(2)=1.
    Find the value of each of the following at x=2:

    a) (2f-3g)'

    b) (2f-3g)''

    c) (fg)'

    Would I be right by saying that I need to do something like this:

    (2f-3g)'=2f'-3g'=2(4)-3(2)=2 ?

    Could someone give a small lecture on what's happening here?

    Thankx.
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  2. #2
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    Quote Originally Posted by VonNemo19 View Post
    Suppose that f and g are functions such that:

    f(2)=-1, f'(2)=4, f''(2)=-2, g(2)=-3, g'(2)=2, g''(2)=1.
    Find the value of each of the following at x=2:

    a) (2f-3g)'

    b) (2f-3g)''

    c) (fg)'

    Would I be right by saying that I need to do something like this:

    (2f-3g)'=2f'-3g'=2(4)-3(2)=2 ? Mr F says: Yes.

    Could someone give a small lecture on what's happening here?

    Thankx.
    You seem to have the idea, so what's to say? Find the required derivatives. Substitute x = 2. Use the given values to evaluate the derivatives.
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  3. #3
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by mr fantastic View Post
    You seem to have the idea, so what's to say? Find the required derivatives.
    You really are a rascal!

    O.K.

    So for c) then...

    f'g+g'f=4(-3)+2(-1)=-14 ?
    Last edited by mr fantastic; June 20th 2009 at 05:42 PM. Reason: Off-topic
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  4. #4
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    Quote Originally Posted by VonNemo19 View Post
    You really are a rascal!

    O.K.

    So for c) then...

    f'g+g'f=4(-3)+2(-1)=-14 ?
    Yes to both.
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  5. #5
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    At some point, very early in your Calculus class, you should learn:

    (f+ g)'= f'+ g'
    (f- g)'= f'- g'
    (fg)'= f'g+ fg'
     (f/g)'= (f'g- fg')/g^2
    You need the first three of those here.
    Last edited by HallsofIvy; June 21st 2009 at 07:11 AM.
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  6. #6
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by HallsofIvy View Post
    At some point, very early in your Calculus class, you should learn:

    (f+ g)'= f'+ g'
    (f- g)'= f'- g'
    (fg)'= f'g+ fg'
     (f/g)'= (f'g- fg')/g^2
    You need the first three of those here.
    Yeah, I know that. I even understand the proofs behind the elementary differentiation formulas. It's just that, when I initially looked at this problem, I was confused because of the notation used. We were studying the derivatives of inverse functions at the time, and then my techer threw this gem in there. Threw me for a loop.
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