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

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
$

The statement is wrong, of course; at $\displaystyle x=0$ we do have equality, whereat $\displaystyle \cos x\ge1-x$ holds for all $\displaystyle x\ge0.$