Consider a non-negative function $f(x)$ which is continuous and bounded over the interval $[2,8]$. Let $M$ and $m$ denote, respectively, the maximum and the minimum values of $f(x)$ over the interval.
Among the combinations of $\alpha$ and $\beta$ given below, choose the one(s) for which the inequality
$$ \beta \leq \int_{2}^{8} f(x) d x \leq \alpha$$
is guaranteed to hold.
- $\beta=5 m, \alpha=7 M$
- $\beta=6 m, \alpha=5 M$
- $\beta=7 m, \alpha=6 M$
- $\beta=7 m, \alpha=5 M$
