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Homework Help: Find local maximum value

  1. Sep 3, 2015 #1
    1. The problem statement, all variables and given/known data
    y=(8/5)sint + (4/5) cost - (9/5)e^(-t/2)

    find its local max
    2. Relevant equations

    3. The attempt at a solution
    i have differentiated it and found out dy/dx,
    in order to find the local max, i have to find out the value t when dy/dx=0
    but i cant solve this equation
  2. jcsd
  3. Sep 3, 2015 #2


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    Homework Helper

    Local in what neighborhood? I don't see any x in the problem you posted, what is dy/dx?
    Note that as t gets large, you can neglect the exponential term. Then you can easily solve the trigonometric equation.
  4. Sep 3, 2015 #3

    Ray Vickson

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    Science Advisor
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    Of course, dy/dx = 0 because your y does not contain any x variable. However, if you mean dy/dt then I agree, you have an "unsolvable" problem, in the sense that there will be no nice closed-from solution. However, you can use numerical methods.

    In such cases, always start by plotting a graph of your function, to get a feel for what is happening. Plotting the derivative can be helpful, too.

    BTW: your post is mis-named. You do not have a differential equation, you just have a given function that you want to differentiate.
  5. Sep 3, 2015 #4


    Staff: Mentor

    I changed the thread title...
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