Answer
a) If $f$ is continuous on a closed interval $[a, b]$, then $f$ attains an absolute maximum value $f(c)$ and an absolute minimum value $f(d)$ at some numbers $c$ and $d$ in $[a, b]$.
b) The closed interval method works to show the existence of extreme values along a closed interval, operating based off of the properties of a continuous function along a bounded interval as established by the Extreme Value Theorem.
Work Step by Step
Being able to state the theorem is a matter of memorization, and the application of it is also memorization.