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Math Help - A little derivative help (definition of derv.)

  1. #1
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    A little derivative help (definition of derv.)

    Hey guys, I'm using the definition of derivative to find f'(a), this always makes a mess. This is what I have done so far;

    Question: f(t) = 2t3+t, find f'(a).

    So,

    lim f(a+h)-f(a)/(h) - the formula
    h->0

    lim 2(a+h)+(a+h)-(2(a)3+a)/(h)
    h->0


    Here's all the foiling etc I did on the side:

    (a+h)(a+h)(a+h)
    (a2+2ah+h2)(a+h)
    eventually getting....2(a3+3a2h+3ah2+h3) = 2a3+6a2h+6ah2+2h3

    so now I have,

    lim 2a3+6a2h+6ah2+2h3+a-h-2a3-a/(h)
    h->0

    lim 6a2​h+6ah2+2h3-h/(h)
    h->0

    lim 6a2h+6ah2+2h3
    h->0

    6a2(0)+6a(0)2+2(0)3-1 = -1


    f'(a) = -1?

    Not sure where I went wrong, the derivative of 2t3​+t is definitely not -1. Could use some guidance.

    Thank you.


    Ok so I figured out that I missed a step, after

    lim 6a2h+6ah2+2h3-h/(h)
    h->0

    I should have isolated h so I get

    lim h(6a2+6ah+2h2-1)/h (now cancel out the h's)
    h->0


    lim 6a2-6ah-2h2+1
    h->0

    6a2-0-0+1

    = 6a2​+1 how does this look?

    Last edited by Oldspice1212; May 14th 2013 at 05:47 PM.
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: A little derivative help (definition of derv.)

    Looks good!
    Thanks from Oldspice1212
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    Re: A little derivative help (definition of derv.)

    Quote Originally Posted by MarkFL View Post
    Looks good!
    Lol thanks, these question are a pain in the butt >.<
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