Toolkit 98

Bounding the Answer

When finding a minimum, maximum, or extremal value, think of the answer as lying in a range.

LAnswerUL\leq \text{Answer}\leq U

Proof → establish a bound.

Example → attain a bound.

Improve both bounds until they become equal.

L=UAnswer=LL=U\quad\Longrightarrow\quad \text{Answer}=L