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Max/min with trig funtions problem

  1. May 29, 2009 #1
    1. The problem statement, all variables and given/known data

    Within the interval ( -22.27, 40.55 ), for what value of x does f(x) take on a minimum if
    f(x)=4.7sin(0.1x)−6.1cos(0.1x)

    Later the question asks for the maximum as well.

    2. The attempt at a solution

    I know to find the critical values to take the first derivative and set it equal to zero, then solve for x. When I do that I get the equation...

    0=.47cos(.1x)+.61sin(.1x)

    When I solve this guy, by manipulating the equation to get tan(.1x)=-.47/.61, I get only one value, x=-6.56487, which is the minimum value. But I also need a maximum value. I've tried both end points within the interval and they were wrong. Is there something I'm missing here?

    Any help would be appreciated.
     
  2. jcsd
  3. May 29, 2009 #2

    CompuChip

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    Science Advisor
    Homework Helper

    The tangent is a periodic function.
    What is the period of tan(0.1 x)?
    One period beyond x = -6.5... there will be another solution which is also in the given interval.
     
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