Results 1 to 8 of 8

Math Help - average velocity and Mean Value Theorem

  1. #1
    Member cassiopeia1289's Avatar
    Joined
    Aug 2007
    From
    chicago
    Posts
    101

    average velocity and Mean Value Theorem

    ok, couple problems:

    they give you a graph of velocity [IMG]file:///C:/DOCUME%7E1/student/LOCALS%7E1/Temp/moz-screenshot-1.jpg[/IMG] [IMG]file:///C:/DOCUME%7E1/student/LOCALS%7E1/Temp/moz-screenshot-2.jpg[/IMG]
    they ask: what is the average velocity of the plane during the two hour flight? - now, would I just use \frac{1}{2-0}\int_{0}^{2}{f(x)dx}
    but that would find average distance though, wouldn't it? not velocity

    next question:
    f(x) = 3x^3 - 5x^2 + 2x + 2
    Use graph of f(x) to estimate the value(s) of "c" guaranteed by Mean Value Theorem on interval [-1, 2]
    Now, I know that \int_{a}^{b}{f(x)dx = f(c)(b-a)}
    so set up is \int_{-1}^{2}{f(x)dx = f(c)(3)} but then I'm stuck - should I integrate? how do I know what c is supposed to be?
    the next question asks: Find the value(s) of "c" analytically.
    Um ... help
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by cassiopeia1289 View Post
    ok, couple problems:

    they give you a graph of velocity [IMG]file:///C:/DOCUME%7E1/student/LOCALS%7E1/Temp/moz-screenshot-1.jpg[/IMG] [IMG]file:///C:/DOCUME%7E1/student/LOCALS%7E1/Temp/moz-screenshot-2.jpg[/IMG]
    they ask: what is the average velocity of the plane during the two hour flight? - now, would I just use \frac{1}{2-0}\int_{0}^{2}{f(x)dx}
    but that would find average distance though, wouldn't it? not velocity

    next question:
    f(x) = 3x^3 - 5x^2 + 2x + 2
    Use graph of f(x) to estimate the value(s) of "c" guaranteed by Mean Value Theorem on interval [-1, 2]
    Now, I know that \int_{a}^{b}{f(x)dx = f(c)(b-a)}
    so set up is \int_{-1}^{2}{f(x)dx = f(c)(3)} but then I'm stuck - should I integrate? how do I know what c is supposed to be?
    the next question asks: Find the value(s) of "c" analytically.
    Um ... help
    No it would find average velocity because you integrate losing a "time" but then remember you are dividing by time when you do \frac{1}{b-a}

    So you have \int_a^{b}f(t)dt where f(t) is velocity...we integrate and lose a time...to get s(t) but then to get average we divide by the 1/(b-a) giving us distance over time which is velocity.,..make sense?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by cassiopeia1289 View Post
    ok, couple problems:

    they give you a graph of velocity [IMG]file:///C:/DOCUME%7E1/student/LOCALS%7E1/Temp/moz-screenshot-1.jpg[/IMG] [IMG]file:///C:/DOCUME%7E1/student/LOCALS%7E1/Temp/moz-screenshot-2.jpg[/IMG]
    they ask: what is the average velocity of the plane during the two hour flight? - now, would I just use \frac{1}{2-0}\int_{0}^{2}{f(x)dx}
    but that would find average distance though, wouldn't it? not velocity

    next question:
    f(x) = 3x^3 - 5x^2 + 2x + 2
    Use graph of f(x) to estimate the value(s) of "c" guaranteed by Mean Value Theorem on interval [-1, 2]
    Now, I know that \int_{a}^{b}{f(x)dx = f(c)(b-a)}
    so set up is \int_{-1}^{2}{f(x)dx = f(c)(3)} but then I'm stuck - should I integrate? how do I know what c is supposed to be?
    the next question asks: Find the value(s) of "c" analytically.
    Um ... help
    I think for the second part you are a little mixed up...you are thinking of the mean-value theorem for integrals....I think based on the first part of the question you are supposed to be using the mean-value theroem for slope that states there is at least one point c on an interval where the slope equals the average slope...so take your answer to a...and set it equal to your velocity equation and solve for c
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member cassiopeia1289's Avatar
    Joined
    Aug 2007
    From
    chicago
    Posts
    101
    these are actually two separate problems
    the graph and velocity is number 11 and the second two questions are number 23
    they're not related
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by cassiopeia1289 View Post
    these are actually two separate problems
    the graph and velocity is number 11 and the second two questions are number 23
    they're not related
    Well then you will have to guess by the context of your chapter which mean-value theorem they mean....so what you do for your case is evaluate teh integral on teh left side of you equation then set it equal to f(c)(b-a) and solve for
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member cassiopeia1289's Avatar
    Joined
    Aug 2007
    From
    chicago
    Posts
    101
    ok, so it is the mean value theorem I was thinking beforehand

    and then how do you find it analytically vs. setting them equal to each other (which I thought was analytically)
    Last edited by cassiopeia1289; April 27th 2008 at 01:24 PM.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by cassiopeia1289 View Post
    ok, so it is the mean value theorem I was thinking beforehand then?

    and then how do you find it analytically vs. setting them equal to each other (which I thought was analytically)
    \int_{-1}^{2}f(x)dx=\frac{21}{4}

    now we ahve \frac{21}{4}=f(c)(b-a)=f(c)(2+1)=3f(c)

    f(c)=3c^3-5c^2+2c+2=\frac{7}{4}
    i divided by the three if you cant see how I got 7/4

    now solve for c
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Member cassiopeia1289's Avatar
    Joined
    Aug 2007
    From
    chicago
    Posts
    101
    fabulous - I got that part
    thats not really my problem

    its the difference between analytically verses "estimation"
    what am I to look for for "estimation" - what, I mean, on the graph would be an indicator of the "c" value?
    what you just showed was analytical
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Average velocity
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 8th 2010, 02:02 PM
  2. Replies: 3
    Last Post: February 20th 2010, 07:21 PM
  3. average velocity!!
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: January 12th 2009, 10:22 AM
  4. average velocity
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: October 6th 2008, 08:45 PM
  5. [SOLVED] Can the average velocity and delta velocity ever be the same?
    Posted in the Advanced Applied Math Forum
    Replies: 9
    Last Post: September 28th 2007, 05:24 AM

Search Tags


/mathhelpforum @mathhelpforum