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Homework Help: Solving an intial value problem using relative extrema

  1. Sep 5, 2012 #1
    1. The problem statement, all variables and given/known data
    See uploaded file. PROBLEM 5


    2. Relevant equations
    See uploaded file


    3. The attempt at a solution
    I am confused on how to go about doing the rest of this I realize I can do it with the first and second derivatives but I forgot what exactly I do with that. I know the first derivative gives me a tangent line to the curve or should I use limits to do this? SEE PROBLEM 5
     

    Attached Files:

    Last edited: Sep 6, 2012
  2. jcsd
  3. Sep 6, 2012 #2

    ehild

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    I do not understand what you tried to do. The problem asks the numerical value of y at t=0.8.
    What is the value of the first derivative at a local maximum or minimum? Substitute it for y' in the equation.

    ehild
     
  4. Sep 6, 2012 #3
    ok so should I scap my work or just plug .8 into the first derivative of what I did?
     
  5. Sep 6, 2012 #4

    ehild

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    Answer my question, please. What is the numerical value of the first derivative of any function at a local extreme?

    ehild
     
  6. Sep 6, 2012 #5
    Ok man you got me I really am trying so at a local extreme there has to be a critical point so the value of the derivative at that point equals zero correct?
     
  7. Sep 6, 2012 #6
    ok so by setting y'=0 and solving for y I get -1.34909.
     
  8. Sep 7, 2012 #7

    ehild

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    Correct.
    You can solve the differential equation, too (although it is not asked) and use this value of y at t=0.8 to get the integration constant. And then the full y(t) function is known.

    ehild
     
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