Find the maximum and minimum value of the function $f(x)=\binom{16-x}{2x-1}+\binom{20-3x}{4x-5}.$
ATTEMPT:-
By A.M.-G.M. inequality, $\frac{a+b}{2}\ge\sqrt{ab}$, $\quad$ for $a,b\gt 0$ with equality at $a=b.$
For minimum value, $\binom{16-x}{2x-1}=\binom{20-3x}{4x-5}.$
$\qquad$$\implies x=2.$
But when I use my graphing calculator, I get a different result.Where am i going wrong?
And how do I calculate the maximum value?