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Math Help - General derivative functions

  1. #1
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    General derivative functions

    Hi, I'm starting derivatives and I am getting confused. Some problems seem easier solved by

    f(x)-f(a)
    ---------
    x - a

    As x approaches a

    and some by

    f(a+h)-f(a)
    -----------
    h

    as h approaches 0

    Why is this and how do I choose the best option? Does it matter if it's a velocity problem and not a tangent problem? I thought they were the same. Does it matter if I have a point (c,f(c)) to go off of? I apologize if I'm not making much sense, but I have practiced both methods and still don't understand why they are different.
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  2. #2
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    Re: General derivative functions

    The first one gives you the gradient between two points - a linear type profile.

    The later can be used to find the gradient at any point on a curve - nonlinear
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  3. #3
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    Re: General derivative functions

    The two definitions are quite similar. Let x = a+h for some small h and you'll see what I mean.
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  4. #4
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    Re: General derivative functions

    Ok. I think I understand. One is a secant line and one is a limit. Right? Or are they both limits? Are these two completely interchangeable? Say I have the function g(x)=x^2+3x+2. I get the same answer when using either method: 2a+3. However it was easier for me to use the h\rightarrow0 method because it didn't require polynomial division like the other one did.

    Thank you for all your help.
    Last edited by rortiz81; June 28th 2012 at 02:54 PM.
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  5. #5
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    Re: General derivative functions

    They should be the same, or roughly the same...I don't see why one definition would be significantly different from the other.
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