Greatest value of f If $f'(x)=6-x$ then which of the following has the greatest value?


*

*$f(2.01)-f(2)$

*$f(3.01)-f(3)$

*$f(4.01)-f(4)$

*$f(5.01)-f(5)$

*$f(6.01)-f(6)$
I know the answer is $f(2.01)-f(2)$ but how to prove?

Hint:Use the 
$$f'(x)\approx \frac{f(x+h)-f(x)}{h}$$ with $h=0.01$.
