Results 1 to 3 of 3
Like Tree2Thanks
  • 2 Post By Debsta

Thread: Please help me with a problem about particular antiderivatives?

  1. #1
    Junior Member
    Joined
    Sep 2018
    From
    Philippines
    Posts
    27

    Please help me with a problem about particular antiderivatives?

    Hi everyone. I'm stuck with this problem on particular antiderivatives:

    "The points (1,3) and (0,2) are on a curve, and at any point (x,y) on the curve, d2y/dx2 = 2 - 4x. Find an equation for the curve."

    I was able to get dy/dx from solving, and I got 2x - 2x2 + C. Now I'm unsure what to do... I did, however, try and guess my way through the problem (oops). I eventually came up with the final answer of y = x2 - 2x3/3 - 2x + 14/3. If it happens to actually be the answer, please tell me.

    Can someone please lead me in the right direction? Thank you so much!

    NOTE: Attached is my solution to the problem just in case you would like to see how I got my (guessed) final answer.
    Attached Thumbnails Attached Thumbnails Please help me with a problem about particular antiderivatives?-particular-antiderivatives.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    From
    Brisbane
    Posts
    1,245
    Thanks
    462

    Re: Please help me with a problem about particular antiderivatives?

    Quote Originally Posted by kaonashi View Post
    Hi everyone. I'm stuck with this problem on particular antiderivatives:

    "The points (1,3) and (0,2) are on a curve, and at any point (x,y) on the curve, d2y/dx2 = 2 - 4x. Find an equation for the curve."

    I was able to get dy/dx from solving, and I got 2x - 2x2 + C. Now I'm unsure what to do... I did, however, try and guess my way through the problem (oops). I eventually came up with the final answer of y = x2 - 2x3/3 - 2x + 14/3. If it happens to actually be the answer, please tell me.

    Can someone please lead me in the right direction? Thank you so much!

    NOTE: Attached is my solution to the problem just in case you would like to see how I got my (guessed) final answer.
    You can check your answer by checking whether the points (1, 3) and (0, 2) satisfy the equation. Clearly (0, 2) doesn't (sub in x=0 and you don't get 2).

    You were correct in finding $\displaystyle \frac{dy}{dx} = 2x - 2x^2 + c $

    Now do it again to find $\displaystyle y = x^2 -\frac{2}{3}x^3 + cx +d $

    Sub in your 2 points, gives two equations with two unknowns, solve for c and d.

    No guesswork involved.
    Thanks from kaonashi and topsquark
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Sep 2018
    From
    Philippines
    Posts
    27

    Re: Please help me with a problem about particular antiderivatives?

    Thank you very much!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: Mar 31st 2019, 06:05 PM
  2. Determing Antiderivatives from a Word Problem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Jan 22nd 2014, 06:27 AM
  3. Replies: 5
    Last Post: Dec 17th 2012, 07:26 PM
  4. Antiderivatives word problem!
    Posted in the Calculus Forum
    Replies: 5
    Last Post: Nov 28th 2010, 06:41 PM
  5. Antiderivatives Problem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: Nov 25th 2009, 06:43 AM

/mathhelpforum @mathhelpforum