Results 1 to 3 of 3

Math Help - derivatives/ implicit differentiation

  1. #1
    Junior Member
    Joined
    Oct 2007
    Posts
    36
    Awards
    1

    derivatives/ implicit differentiation

    I tried to work out this problem and I got some answers, but I'm highly doubtful about them. Can someone reassure me please.

    An Object is moving along the parabola y=3x^2
    a) when it passes through point (2,12), its horizontal velocity is dx/dt=3. What is its vertical velocity at that instant?
    b) If it travels in such a way that dx/dt=3 for all t, then what happens to dy/dt as t approaches (+)infinity?
    c) If, however, it travels in such a way that dy/dt remains constant, then what happens to dx/dt at t approaches (+)infinity?

    My Work:
    a) dy/dt=6*x*(dx/dt)
    dy/dt=6*2*3=36 ?

    b) dy/dt=6*x*(dy/dt)
    dy/dt=6*x*3=18x ?

    c) ?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by coe236 View Post
    I tried to work out this problem and I got some answers, but I'm highly doubtful about them. Can someone reassure me please.

    An Object is moving along the parabola y=3x^2
    a) when it passes through point (2,12), its horizontal velocity is dx/dt=3. What is its vertical velocity at that instant?
    b) If it travels in such a way that dx/dt=3 for all t, then what happens to dy/dt as t approaches (+)infinity?
    c) If, however, it travels in such a way that dy/dt remains constant, then what happens to dx/dt at t approaches (+)infinity?

    My Work:
    a) dy/dt=6*x*(dx/dt)
    dy/dt=6*2*3=36 ?
    correct


    b) dy/dt=6*x*(dy/dt)
    dy/dt=6*x*3=18x ?
    we are traveling in the positive direction, since dx/dt is positive. this means as t gets larger, x also gets larger. but dy/dt depends on x, so as x gets very large, so does dy/dt. it will goes to infinity.

    c) ?
    it would have to get smaller. as t gets large, so does x. since x is getting large, we want dx/dt to keep getting smaller so we can maintain a constant dy/dt
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Oct 2007
    Posts
    36
    Awards
    1
    that makes sense. Thanks!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: October 17th 2010, 03:30 PM
  2. Replies: 2
    Last Post: July 26th 2010, 05:24 PM
  3. Higher Derivatives & Implicit Differentiation
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 15th 2010, 02:05 PM
  4. Replies: 5
    Last Post: April 13th 2010, 02:07 PM
  5. Replies: 1
    Last Post: October 10th 2008, 07:29 AM

Search Tags


/mathhelpforum @mathhelpforum