Practice question · Put in order
Order the steps of the closed interval method for absolute extrema.
- Find all critical points of f inside (a, b)
- The largest value is the absolute maximum; the smallest is the absolute minimum
- Evaluate f at each critical point
- Evaluate f at the endpoints a and b
Hints
- You must collect candidate points before you can compare their values.
- Comparison comes last, once every candidate has been evaluated.
Show the answer
- Find all critical points of f inside (a, b)
- Evaluate f at each critical point
- Evaluate f at the endpoints a and b
- The largest value is the absolute maximum; the smallest is the absolute minimum
Why
On a closed bounded interval a continuous function always attains its extreme values.
Practise Extrema and optimization
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