Suppose a two digit whole number is divided by the sum of its digits, what are the largest and smallest possible values? So we can write a two digit whole number as $n = 10a+b$ where $1 \leq a,b \leq 10$ and we would have that we want to minimize/maximize the following functions:
$f(a,b) = 10a+b$
$g(a,b) = a+b$
I don't remember how one does this and I don't know if there is another approach that could work.