Quick calc question

Find the x-coordinates where f '(x) = 0 for f(x) = 2x + sin(4x) in the interval [0, π].

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asked by Mel
  1. dy/dx = 2 + 4 cos 4 x

    so
    cos 4x = -1/2

    4x = 180 - 60 degrees = 120
    degrees = (2/3) pi
    so x = pi/6
    or
    4x = 180+60 or 4 pi/3
    so x = pi/3
    4 x = 360+180 - 60 = 480 =8 pi/3
    so x = 2 pi/3
    4 x = 360+180 + 60 = 600 = 10 pi/3
    so x = 5 pi/6 too big
    so
    pi/6 , pi/3 , 2 pi/3

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    posted by Damon

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