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Math Help - Extreme values of this trig function

  1. #1
    Junior Member
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    Extreme values of this trig function

    Find the absolute extreme values of y=cos(x) + sin(x) on the interval 0 to 2pi

    y'=cos(x) - sin(x)

    y'=0 when x= pi/4

    However, the answer in the book is max: sqrt{2} min: -sqrt{2)

    P.S. Is it just me or am I getting a latex error?
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  2. #2
    MHF Contributor
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    Hi

    You don't need to take the derivative
    y=cos(x) + sin(x)=sqrt(2) (sqrt(2)/2 . cos(x) + sqrt(2)/2 . sin(x)) = sqrt(2) (sin(pi/4) . cos(x) + cos(pi/4) . sin(x)) = sqrt(2) sin(x+pi/4)

    Otherwise with the derivative
    y'=cos(x) - sin(x)

    y'=0 when x= pi/4 (mod 2pi) or x=5pi/4 (mod 2pi)
    y(pi/4) = sqrt(2)
    y(5pi/4) = -sqrt(2)

    Quote Originally Posted by IanCarney View Post
    P.S. Is it just me or am I getting a latex error?
    The problem is known. Admins are trying to fix it.
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