# Mean Value Theorem

• 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.

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 $
x > 0 \Rightarrow f(x) > f(0)
$
I mean: $\cos x +x-1>cos0 +0-1=0$ $
\Leftrightarrow \cos x > 1 - x
$
• 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 $x\ge0.$