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Absolute Extrema

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Find the minimum and maximum values of the function f(x)= 2/3 sin pix on the interval [1,2] (domain).

I got (1.5, -2/3) as the minimum and no maximum on the interval. Is it correct? Thank you.

  • Absolute Extrema -

    correct.

  • Absolute Extrema -

    I bet you mean

    f(x) = (2/3) sin(pi x)

    f'(x) = (2/3) pi cos(pi x)
    f'(x) = 0 for max or min

    that is when cos (pi x) = 0
    x = 1/2 and x = 3/2

    if x = 1/2
    y = (2/3)sin (pi/2) = 2/3

    if x = 3/2
    y = (2/3) sin (3 pi/2) = -2/3

    PS
    You can be sure that the max and min of a sin function are +1 and -1

  • Absolute Extrema -

    sorry, x = 1/2 not in domain so you are right

  • Absolute Extrema -

    Thank you both! I appreciate it. :)

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