Results 1 to 3 of 3
Like Tree2Thanks
  • 1 Post By HallsofIvy
  • 1 Post By skeeter

Thread: differentiation

  1. #1
    Newbie
    Joined
    Jul 2017
    From
    US
    Posts
    21

    differentiation

    hi everyone....i have this question to ask....i dont even know how to start for this question....can anybody help me?

    Sent from my Lenovo A5000 using Tapatalk
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    19,455
    Thanks
    2892

    Re: differentiation

    I would hope that you know that the volume of any such prism, with a base of area, A (here the triangular side), and length, l, has volume V= Al. The rate of change of volume, dV, is given, using the product rule, by dV= l dA+ A dl. Now put the information you are given into that equation.
    Thanks from goldsomecriss
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    16,191
    Thanks
    3687

    Re: differentiation

    This is a related rates problem. You are given $\dfrac{dV}{dt} = -27 \, cm^3/sec$ and $\dfrac{db}{dt} = 2 \, cm/sec$. The problem statement gives no info about the length of the prism, $L$, so I'm making the assumption it's not changing (remains a constant).

    The problem wants to know if $h$ is increasing or decreasing when $b = 6 \, cm$ and $h = 3 \, cm$

    First, let's use some common sense. The volume has a decreasing rate of change while the base length has an increasing rate of change ... what would you say is happening to the height?



    Doing the calculation, the volume of the prism is $V = \dfrac{1}{2}bh \cdot L$ where $L$, the prism length, is a constant.

    Take the derivative of the above volume formula implicitly w/respect to time and determine the value of $\dfrac{dh}{dt}$ in terms of $L$.


    Oh ... next time post calculus problems in the calculus forum.
    Attached Thumbnails Attached Thumbnails differentiation-related-rates-1.jpg  
    Thanks from goldsomecriss
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: Jul 26th 2010, 06:24 PM
  2. Differentiation and partial differentiation
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 30th 2010, 11:16 PM
  3. Differentiation and Implicit Differentiation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Feb 6th 2009, 05:07 AM
  4. differentiation help
    Posted in the Calculus Forum
    Replies: 3
    Last Post: Oct 12th 2008, 08:03 AM
  5. Differentiation
    Posted in the Calculus Forum
    Replies: 6
    Last Post: Sep 24th 2008, 04:07 AM

/mathhelpforum @mathhelpforum