Also the end points 0 and 6 are critical points.

End points are not critical points. A point** x** is a critical point if it satisfies either of the following conditions:

- $f'(x)=0;$
- $f'(x)$ is undefined.

Here we do check for endpoints because they are included in the domain (closed interval).

The endpoints require separate treatment: There is the auxiliary point to just $t_{0}$ the *right* of the left endpoint **a**, and the auxiliary point $t_{n}$ just to the *left* of the right endpoint **b**:

- At the
*left*endpoint**a**, if $f'(t_{0})< 0$ (so $f'$ is*decreasing*to the right of**a**) then**a**is a*local maximum*. - At the
*left*endpoint**a**, if $f'(t_{0})> 0$ (so $f'$ is*increasing*to the right of**a**) then**a**is a*local minimum*. - At the
*right*endpoint**b**, if $f'(t_{n})< 0$ (so $f'$ is*decreasing*as**b**is approached from the left) then**b**is a*local minimum*. - At the
*right*endpoint**b**, if $f'(t_{n})> 0$ (so $f'$ is*increasing*as**b**is approached from the left) then**b**is a*local maximum*.

Source: https://mathinsight.org/local_minima_maxima_refresher

Now what if end-points are not included in the domain (open interval)?