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Math Help - Intervals of increase and decrease

  1. #1
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    Intervals of increase and decrease

    interval -pi<=x<=pi
    y=cosx-sinx
    dy/dx= -sinx-cosx
    sinx=-cosx
    cosx=-sinx
    tanx=-1
    two angles are -pi/4 and 3pi/4

    I am stuck here. Normally i would use a table to determine the period of increase and decrease from y'. How do you set up the table in this case?
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  2. #2
    MHF Contributor Calculus26's Avatar
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    use a graph

    Set up a graph for the derivative -sin(x) -cos(x) on (-pi,pi)

    you already know the zeroes--so just look where the graph is positive

    If you must use a table consider -pi to pi/4, -pi/4 to 3pi/4 and 3pi/4 to pi
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  3. #3
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    Quote Originally Posted by justin016 View Post
    interval -pi<=x<=pi
    y=cosx-sinx
    dy/dx= -sinx-cosx
    sinx=-cosx
    cosx=-sinx
    tanx=-1
    two angles are -pi/4 and 3pi/4

    I am stuck here. Normally i would use a table to determine the period of increase and decrease from y'. How do you set up the table in this case?
    [-pi ............-pi/4..............3pi/4.............pi]

    pick a value in each interval, and determine the sign of y' in that interval.

    first interval, y'(-pi) > 0 ... y is increasing

    second interval, y'(0) < 0 ... y is decreasing

    third interval, y'(pi) > 0 ... y is increasing
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