mathematics

When the graph of y equal to 3cos2x achieves minimum what is the value of the y coordinate

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  1. In point where firs derivative = 0
    function have loca minimum or maximum.

    If second derivative < 0 that is local maxsimum.

    If second derivative > 0 that is local minimum.

    If expression 3cos2x mean :

    3 cos (2 x )

    then first derivative =

    - 6 sin ( 2 x )

    - 6 sin( 2 x ) = 0 when

    sin ( 2 x ) = 0

    sin theta = 0 when theta = 0

    in this case 2 x = 0

    when x = 0 or x = pi / 2

    The period of sin x is 2 n pi

    The period of sin ( 2 x ) is n pi

    where n is some intefer number

    So - 6 sin( 2 x ) = 0 when

    x = n pi + 0 = n pi

    or

    x = n pi + pi / 2

    or

    x = n pi - pi / 2

    Second derivative = - 12 cos ( 2 x )

    For x = n pi second derivative < 0

    for that's values of x function have maximum

    For x = n pi + pi / 2 second derivative > 0

    and

    For x = n pi - pi / 2 second derivative > 0

    for that's values of x function also have minimum

    So function 3 cos (2 x ) have local minimums when

    x = n pi + pi / 2

    and

    x = n pi - pi / 2

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  2. Given y = 3cos2x

    you know it has amplitude of 3, so its minimum value is y = -3, since there is no y-translation.

    Unless you are specifically doing calculus, I'd surely use my knowledge of trig to answer this one.

    Good analysis, though, Bosnian!

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