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Math Help - Mean Value Theorum

  1. #1
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    Mean Value Theorum

    Hi
    I'm studying for my midterm and am really confused.
    One ofthe practice questions is that I am supposed to show that
    lsinx-sinyl 'is less than or equal to' lx-yl
    using the Mean Value Theorum.
    I thought the mean value theorum is pretty much this.
    so lsinx-sinyl/lx-yl is less than or equal to zero
    meaning the derivative of f(t)=sint is less than zero
    so cos(t) is less that zero. Okay, so cos(t)=lsinx-sinyl/lx-yl
    and now I'm stuck. How do I prove this statement. Isn't it a proof of itself?
    Also, do the absolute value signs matter or can I basically just ignore them.
    Thanks!
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  2. #2
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    Quote Originally Posted by sberxa View Post
    Hi
    I'm studying for my midterm and am really confused.
    One ofthe practice questions is that I am supposed to show that
    lsinx-sinyl 'is less than or equal to' lx-yl
    using the Mean Value Theorum.
    I thought the mean value theorum is pretty much this.
    so lsinx-sinyl/lx-yl is less than or equal to zero
    meaning the derivative of f(t)=sint is less than zero
    so cos(t) is less that zero. Okay, so cos(t)=lsinx-sinyl/lx-yl
    and now I'm stuck. How do I prove this statement. Isn't it a proof of itself?
    Also, do the absolute value signs matter or can I basically just ignore them.
    Thanks!
    If x<y then MVT on [x,y] gives \sin y - \sin x = \cos ( z) (y-x) \implies |\sin x - \sin y | = |x-y| |\cos z| where x<z<y. But |\cos z|\leq 1. Thus, |\sin x - \sin y| \leq |x-y|.
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