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Math Help - Minimum and maximum

  1. #1
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    Minimum and maximum

    Calculate minimum and maximum and zeros fo function 3sinx.


    Thanx, by.
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  2. #2
    Senior Member Stroodle's Avatar
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    As the amplitude is 3 and there is no vertical translation or dilation parallel to the x-axis, the maximums would be at \left (\frac{\pi}{2}\pm 2\pi n,\ 3\right ) and the minimums would be at \left (\frac{3\pi}{2}\pm 2\pi n,\ -3\right ) (where n is an integer).

    As for the zeros, there would also be infinitely many, since there is no domain specified.

    If the domain were \left [0,2\pi \right] (i.e. one cycle of this particular function) the zeros would be at 0, \pi and 2\pi

    There's a good guide to basic trig graphs and functions here: http://www.purplemath.com/modules/triggrph.htm
    Last edited by Stroodle; November 28th 2009 at 02:16 AM. Reason: Added link
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  3. #3
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    since there is no specified domain, i will make this general:

    zeros occur when sin3x=0,
    so y=sin3x crosses 0 when x=....-60,0,60, 120.... => x=kpi/3 where k is an integer

    to find max/mins we differentiate y=sin3x
    you get y'=3cos3x

    when y'=0 you get stationary => max/min
    3cos3x=0, when x=....,-90, -30,30, 90... => (2k-1)pi/6
    the mins and maxes alternate (max when k is odd, and min when k is even)

    edit: sorry misread Q, thought it was sin3x, but it is actually 3sinx, but i will still leave this incase anyone needs it
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