Results 1 to 5 of 5

Math Help - function of a derivative

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    5

    Post function of a derivative

    find a function whose derivative is 20x^3 plus 6x^2 plus 5
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Dec 2008
    From
    Scotland
    Posts
    901
    Quote Originally Posted by eduk8tedidiot View Post
    find a function whose derivative is 20x^3 plus 6x^2 plus 5

    What you want to find here is the 'anti-derivative' of the function. The integral of a derivative gives you the antiderivative.

    Hence, if we are seeking function  f(x) , then

     f(x) = \int 20x^3 + 6x^2 + 5 \, dx
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Banned
    Joined
    May 2009
    Posts
    471
    Quote Originally Posted by eduk8tedidiot View Post
    find a function whose derivative is 20x^3 plus 6x^2 plus 5

    Have you heard of an integral? Well anyway, we're looking for the anti-derivative of 20x^3+6x+62+5

    In order to get an x^3 the power rule tells us we need an x^4 but the derivative of x^4=4x^3 so we'd have a 4 out in front when we want a 20, so let's put a 5 out in front of our original guess

    Now the derivative of 5x^4=20x^3 so the first term is done....

    Doing similar steps will lead you to an answer of 20x^4+2x^3+5x+c

    Note that when we take the derivative of that, the +c has a derivative of zero, since the question is to find an antiderivative, you can choose any value for c as the answer
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    May 2009
    From
    Zagreb
    Posts
    65
    f'(x) = 20x^3 + 6x^2 + 5

    f(x) = 5x^4 + 2x^3 + 5x + C

    C = konst

    f(x) = a_0 + a_1x + a_2x^2 + ... + a_nx^n

    f'(x) = a_1 + 2a_2x + 3a_3x^2 + ...+ na_nx^{n-1}

    f(x) = C C = const. \rightarrow  f'(x) = 0

    f(x) = kx^m \rightarrow f'(x) = m*k*x^{m-1}
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    Joined
    Dec 2008
    From
    Scotland
    Posts
    901
    Quote Originally Posted by josipive View Post
    f'(x) = 20x^3 + 6x^2 + 5

    f(x) = 5x^4 + 2x^3 + 5x + C

    C = konst

    f(x) = a_0 + a_1x + a_2x^2 + ... + a_nx^n

    f'(x) = a_1 + 2a_2x + 3a_3x^2 + ...+ na_nx^{n-1}

    f(x) = C C = const. \rightarrow  f'(x) = 0

    f(x) = kx^m \rightarrow f'(x) = m*k*x^{m-1}
    Please don't post full solutions.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Derivative of a function
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 24th 2011, 06:48 PM
  2. [SOLVED] Derivative of this function?
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 28th 2010, 11:02 PM
  3. function --- derivative (help!)
    Posted in the Calculus Forum
    Replies: 7
    Last Post: May 23rd 2010, 01:47 PM
  4. derivative of a function
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 20th 2010, 01:30 AM
  5. the derivative function
    Posted in the Calculus Forum
    Replies: 0
    Last Post: February 21st 2010, 07:56 AM

Search Tags


/mathhelpforum @mathhelpforum