$f(x) = x^2 - 6x + 666$

$f'(x) = 2x-6$

1) Find critical points, here $3$ is critical point.

2) find sign in the intervals $(-\infty,3),(3, \infty)$

3) take any values say x=1 in $(-\infty,3)$ then $f'(x)$ is -ve

function is decreasing

4) take any values say x=4 in $(3,\infty)$ then $f'(x)$ is +ve

function is increasing.

$f'(x) = 2x-6$

1) Find critical points, here $3$ is critical point.

2) find sign in the intervals $(-\infty,3),(3, \infty)$

3) take any values say x=1 in $(-\infty,3)$ then $f'(x)$ is -ve

function is decreasing

4) take any values say x=4 in $(3,\infty)$ then $f'(x)$ is +ve

function is increasing.