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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.

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    I changed $\epsilon-\delta$ to $\epsilon$-$\delta$. When the hyphen is _inside_ the $\TeX$ code, then it gets rendered as a minus sign rather as a hyphen.2012-11-12

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