Study the monotonicity of this function The function is $$y=x^2-5x+6$$
I have made
$$[f(x_2)-f(x_1)]/(x_2-x_1)$$
It results in
$$x_1+x_2-5.$$
What should I do next? 

Now suppose that $x_2+h =x_1$ with $ h \to 0$. For a positive monotonicity it has to be 
$$\lim_{h \to 0 } x_1+x_1+h -5\geq 0$$
Solving for $x_1$
$x_1 \geq \frac{5}{2}$
Therefore for $x \geq \frac{5}{2}$ the function is positive monotonic. And for $x < \frac{5}{2}$ the function is strictly negative monotonic.
