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!

I plotted the graph and it show two branches, as you are limiting it to positive values of $a$ it is the right hand branch which is relevant. This shows as crossing the $y-axis$ at the point where $a=0$ and thereafter the curve is decreasing towards the $x-axis$. so putting $a=0$ gives the max value as $13/7$. If you further limit it to positive integer values of $x$ then this occurs for $x=1$ to give a max value of 14/10. 
