f continuous on [a;b]
On a closed interval a continuous function attains a maximum and a minimum. Candidates on that interval:
• endpoints a,b;
• interior points where f′(x)=0;
• interior points where f′ does not exist but f still takes a finite value (corner, etc.).
Then compare numbers: maximum — max, minimum — min over the finite candidate list.
A global maximum on R vs on [a;b] are different setups; do not mix open intervals with [a;b]
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