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Thread: Mean Value Theorem

  1. #1
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    Mean Value Theorem

    Hi

    I think I understand the Mean Value Theorem but the question is "show that cos x >+ 1-x if x>= 0"


    I just don't know where to start or what to do without 2 numbers.

    Please guide me.

    Thanks

    a frustrated Calculus beginner
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  2. #2
    Member Nacho's Avatar
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    Using derivatives:

    You consider $\displaystyle f(x)=\cos x +x-1$ the $\displaystyle f'(x)=-\sin x+1>0$ hence the function is crescente, if $\displaystyle
    x > 0 \Rightarrow f(x) > f(0)
    $ I mean: $\displaystyle \cos x +x-1>cos0 +0-1=0$ $\displaystyle
    \Leftrightarrow \cos x > 1 - x
    $
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  3. #3
    Math Engineering Student
    Krizalid's Avatar
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    The statement is wrong, of course; at $\displaystyle x=0$ we do have equality, whereat $\displaystyle \cos x\ge1-x$ holds for all $\displaystyle x\ge0.$
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