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Find the interval(s) where the function is increasing where and it is decreasing.
f(x)=sin(x+(pi/2)) for 0≤x≤2pi

so my derivative is f'(x)=cos(x+(pi/2))?
and my critical number is -pi/2?

  • Calculus - ,

    cosine is positive for x +pi/2 = 0 to pi/2 and from 3 pi/2 to 2 pi

    when x+pi/2 = 0 then x = -pi/2 or 3pi/2
    when x + pi/2 = pi/2, x = 0
    so one interval is x = 3pi/2 to 0

    when x+pi/2 = 3 pi/2 then x = pi
    when x+pi/2 = 2 pi then x = 3 pi/2

    so second interval is frm x = pi to 3 pi/2

    so finally the entire interval from x = pi to x = 2 pi (which is 0) has a positive derivative, function increasing

  • Calculus - ,

    Wow, so confusing. Thanks!

  • Calculus - ,

    So the whole interval is increasing? The function of cosx has a section of decreasing though.

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