Results 1 to 3 of 3

Math Help - Derivative application

  1. #1
    Junior Member
    Joined
    May 2010
    Posts
    36

    Derivative application

    A rectangular prism has its length increasing by 12 cm/min, its width increasing by 4 cm/min and its height increasing by 2 cm/min. How fast is it's volume changing when the dimensions are 200 cm in length, 50 cm in width and 30 cm in height?


    The following is my working:

    dL/dt = 12 cm/min
    dW/dt = 4 cm/min
    dH/dt = 2 cm/min

    V = L x W x H
    we get:
    V=(200+12t)(50+4t)(30+3t)
    V = 144t^3 + 5460t^2 + 72000t + 300,000
    Derivative of V
    V' = 432t^2 + 10920t + 72000


    Now, I'm very confused. How could we find the rates of change,when 200 cm in length, 50 cm in width and 30 cm in height?

    Thanks!



    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    May 2010
    Posts
    3
    You need to take implicit differentiation of both sides of the volume equation:

    V=L*W*H

    dV/dt = (dL/dt)*W*H + L*(dW/dt)*H + .... (Use chain rule here)

    Then all you need to do is sub in for expressions on the right side and you will get dV/dt which is what you're looking for.

    Hope it helps
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,110
    Thanks
    2
    #1 - Get fluent at writing this sort of thing. It's just the product rule.

    \frac{d}{dt}[L(t)\cdot W(t) \cdot H(t)] = L'(t)\cdot [W(t) \cdot H(t)] + L(t)\cdot [W'(t)\cdot H(t) + W(t)\cdot H'(t)]

    #2 - Or, the Differential Version

    dA = [dL\cdot [W \cdot H] + L\cdot [dW\cdot H + W\cdot dH]]\cdot dt

    Now you fill in the known values:

    dA = 12\cdot [50 \cdot 30] + 200\cdot [4\cdot 30 + 50\cdot 2]

    Did I get them all in the right spots?

    #3 - Really, get good at all three types of notation. Switch effortlessly between them. Let the notation help you.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Application of derivative
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: October 13th 2011, 08:18 PM
  2. Application of derivative help
    Posted in the Calculus Forum
    Replies: 3
    Last Post: September 11th 2009, 07:15 AM
  3. Application of derivative
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 9th 2009, 09:04 PM
  4. Replies: 1
    Last Post: October 9th 2008, 03:17 AM
  5. Application of Derivative
    Posted in the Calculus Forum
    Replies: 4
    Last Post: November 27th 2007, 09:45 PM

Search Tags


/mathhelpforum @mathhelpforum