If $g\in C^1(IR) $ , and $x\leq y$ , such that $g(x)=x$ and $g(y)=y$. Let for some $c\in[x,y]$, such that $|g'(c)|<0.75$. Find the maximum value of $|y-x|$
What I have tried:
Firstly I tried to apply LMV theorem , $g'(c)=\frac{g(y)-g(x)}{y-x}=1$ , but which is not fit with the condition $|g'(c)|<0.75$.
Secondly I just put all the conditions in wolframalpha, I saw a 3D plot there in which I see the maximum value of both $y$ and $x$ are $1.5$ and their minimum is $0$. But I think this one may not be correct.
And, furthermore I think LMV theorem is not applicable here, due to $g\in C^1(IR)$, and sorry to say even I don't know what does this represent. Any help is appreciated. Thanks.