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Math Help - Finding the derivative using the limit defintion.

  1. #1
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    Finding the derivative using the limit defintion.

    Can you help me with this please:

    Using delta/epsilon methods show from definitions that if f(x)= x^3-3x+6 then f`(2)=9.

    Thank you.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by alpha View Post
    Can you help me with this please:

    Using delta/epsilon methods show from definitions that if f(x)= x^3-3x+6 then f`(2)=9.

    Thank you.
    By definition, f'(x) = \lim_{h \to 0} \frac {f(x + h) - f(x)}h or equivalently, f'(a) = \lim_{x \to a} \frac {f(x) - f(a)}{x - a}

    Use either definition along with the \epsilon - \delta definition of a limit that I showed you how to deal with in your last thread.

    You want to show, using the latter definition, for example, \lim_{x \to 2} \frac {x^3 - 3x + 6 - 8}{x - 2} = \lim_{x \to 2} \frac {x^3 - 3x - 2}{x - 2} = 9
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  3. #3
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    I have no idea about this question. can you show me how it is done.

    Thanks again.
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by alpha View Post
    I have no idea about this question. can you show me how it is done.

    Thanks again.
    i already gave you an example of how to tackle problems like this in your last thread. how about you take a crack at it?
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