Remark 1. If the preconditions of the theorem are fulfilled by a function $f$ , then one needs only to determine the values of $f$ in the end points $a$ and $b$ of the interval and in the zeros of the derivative $f'$ inside the interval; then the least and the greatest value are found among those values.

Remark 2. Note that the theorem does not require anything of the derivative $f'$ in the points $a$ and $b$ ; one needs not even the right-sided derivative in $a$ or the left-sided derivative in $b$ . Thus e.g. the function $f:\,x \mapsto \sqrt{1-x^2}$ , fulfilling the conditions of the theorem on the interval $[-1,\,1]$ but not having such one-sided derivatives, gains its least value in the end-point $x = -1$ and its greatest value in the zero $x = 0$ of the derivative.

Remark 3. The least value of a function is also called the absolute minimum and the greatest value the absolute maximum of the function.