Application Of Derivatives

Let a function $f(x)$ be continuous in an interval $[a, b]$. Let $\delta>0$ be a very small real number. Let $c \in(a, b)$ be such that $f(c-\delta)0$. Let $(f(\alpha-\delta)-f(\alpha))(f(\alpha+\delta))<0 \forall \alpha \in(a, b)$ and $\alpha \neq c$. Then,