Let $f(a) = \frac{13+a}{3a+7}$ where $a$ is restricted to positive integers. What is the maximum value of $f(a)$? Let $f(a) = \frac{13+a}{3a+7}$ where $a$ is restricted to positive integers. What is the maximum value of $f(a)$?
I tried graphing but it didn't help.  Could anyone answer?  Thanks!

$f'(a)=-\frac{32}{(3a+7)^2}<0$ so $f$ is strictly decreasing for $a>-\frac73$. So $f(1)>f(2)>f(3)>...$
