Results 1 to 5 of 5

Math Help - [SOLVED] The definition of derivative

  1. #1
    Junior Member
    Joined
    Aug 2008
    Posts
    53

    [SOLVED] The definition of derivative

    Anyone know how to find the derivative using
    5x^3+2


    lim
    x->c

    <br />
\frac {f(x)-f(c)}{x-c}<br />
    Follow Math Help Forum on Facebook and Google+

  2. #2
    o_O
    o_O is offline
    Primero Espada
    o_O's Avatar
    Joined
    Mar 2008
    From
    Canada
    Posts
    1,407
    We are given: f(x) = 5x^3 + 2

    \lim_{x \to c} \frac{{\color{red}f(x)} - {\color{blue}f(c)}}{x - c}

    = \lim_{x \to c} \frac{{\color{red}(5x^3 + 2)} - {\color{blue}(5c^3 + 2)}}{x - c}

    = \lim_{x \to c} \frac{5(x^3 - c^3)}{x - c}

    Recall the difference of cubes formula: a^3 - b^3 = (a - b)(a^2 + ab + b^2)

    Apply that to the numerator and something should cancel out Then you can plug in x = c without worrying about dividing by 0!
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Aug 2008
    Posts
    53
    Does it look something like this?

    <br />
\frac {5(x-c)(x^2+xc+c^2)}{x-c}<br />

    <br />
5(x^2+xc+c^2)<br />

    <br />
5(c^2+(c)(c)+c^2)<br />

    <br />
5(2c^2+c^2)<br />
    Follow Math Help Forum on Facebook and Google+

  4. #4
    o_O
    o_O is offline
    Primero Espada
    o_O's Avatar
    Joined
    Mar 2008
    From
    Canada
    Posts
    1,407
    Don't forget the limit in front of each step!!! :

    = {\color{red}\lim_{x \to c}} \ \frac {5(x-c)(x^2+xc+c^2)}{x-c}

    = {\color{red}\lim_{x \to c}} \ 5(x^2+xc+c^2)

    = 5(c^2 + c^2 +c^2) (You don't need the limit sign here since you already took the limit by replacing x with c)

    And you can simplify the inside by collecting like terms:

    = 5(3c^2) = 15c^2

    So given any point c, the derivative at that point will be 15 times its square
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Aug 2008
    Posts
    53
    i guess i didn't simplify all the way

    i see now

    thanks for the help
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Definition of Derivative/Alt. form of the derivative
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 23rd 2010, 07:33 AM
  2. Replies: 2
    Last Post: September 1st 2010, 03:29 PM
  3. Definition of derivative
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: July 14th 2010, 10:30 PM
  4. Replies: 2
    Last Post: November 6th 2009, 03:51 PM
  5. Derivative using definition
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 28th 2009, 01:06 AM

Search Tags


/mathhelpforum @mathhelpforum