Mean Value Theorem

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March 1st 2009, 09:59 AM
calcbeg

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
March 1st 2009, 10:31 AM
Nacho

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: $\cos x +x-1>cos0 +0-1=0$ $<br /> \Leftrightarrow \cos x > 1 - x<br />$
March 1st 2009, 11:55 AM
Krizalid

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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