#### Answer

minimum average temperature: $51^o\text{ F}$ in January
maximum average temperature: $84^o\text{ F}$ in July

#### Work Step by Step

Locate the minimum and maximum points on the graph of $f(x)$ (refer to the graph below).
The graph shows that the minimum average temperature occurs at $x=1, 13, \text{ and }25$ while the maximumaverage temperature occurs at $x=7\text{ and } 19$.
However, since $x$ represents month, then it would only vary from $x=1$ to $x=12$.
Thus, the minimum average temperature occurs at $x=1$ or in the month of January, which is $51^o\text{ F}$, while the maximum average temperature occurs at $x=7$ or in the month of July, which is at $84^o \text{ F}$..