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Math Help - [SOLVED] Use H-definition to compute the dervative

  1. #1
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    [SOLVED] Use H-definition to compute the dervative

    Use H-definition to compute the dervative F(x)-(3x+1)^2
    Last edited by mr fantastic; May 3rd 2009 at 08:54 PM. Reason: Added post title to post body.
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  2. #2
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    Unless you're referring to the limit process this is all I could drudge up anywhere near "h-definition."


    Here's to just in case.

    \frac{f(x + h) - f(x)}{h}

    \frac{(3(x + h) + 1)^2 - (3x + 1)^2}{h}

    \frac{(9(x + h)^2 + 6(x + h) + 1) - (9x^2 + 6x + 1)}{h}

    \frac{(9x^2 + 18xh + 9h^2 + 6x + 6h + 1) - (9x^2 + 6x + 1}{h}

    \frac{18xh + 9h^2 + 6h}{h}

    18x + 9h + 6

    Now taking the limit as h tends toward 0, 9h gets thrown out and we're left with

    18x + 6

    And surely enough, if you use chain rule:

    2(3x + 1)3 = 18x + 6
    Last edited by mr fantastic; May 3rd 2009 at 08:55 PM. Reason: Merged posts
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  3. #3
    Behold, the power of SARDINES!
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    Quote Originally Posted by Livingg90 View Post
    F(x)-(3x+1)^2
    if you mean the limit definion then

    \lim_{h \to 0}\frac{f(x+h)-f(x)}{h}

    \lim_{h \to 0}\frac{[3(x+h)+1]^2-(3x+1)^2}{h}


    \lim_{h \to 0}\frac{9(x+h)^2+6(x+h)+1-(3x+1)^2}{h}

    \lim_{h \to 0}\frac{9x^2+18xh+9h^2+6x+6h+1-9x^2-6x-1}{h}

    \lim_{h \to 0}\frac{18xh+9h^2+6h}{h}

    \lim_{h \to 0}18x+9h+6=18x+6
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  4. #4
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    thnx
    Last edited by Livingg90; May 3rd 2009 at 08:08 PM.
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