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Math Help - Mean Value Theorem

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