$\epsilon$-$\delta$ proof involving differentiation in a defined neighborhood The problem states: Suppose $f'(b) = M$ and $M <0$. Find $\delta>0$ so that if $x\in (b-\delta, b)$, then $f(x) > f(b).$
This intuitively makes sense, but I am not exactly sure how to find $\delta$. I greatly appreciate any help I can receive.  

Remember that the definition of derivative will imply that
$$
\lim_{x\to b^-}\frac{f(b)-f(x)}{b-x}=M.
$$
But, $M<0$ and $b-x>0$.
