Practice question · Select all that apply
Select every TRUE statement about maxima and minima.
Hints
- Two options make an absolute claim; test both against x cubed and against x to the fourth at 0.
- x to the fourth has f' = 0 and f'' = 0 at 0, and is a genuine minimum.
Show the answer
- A. The 1st-derivative test finds a local max where f' goes + to -
- B. Continuous functions on closed intervals reach global extrema
- D. Global extrema on closed intervals can occur where f' is not 0
Why
Option 1 fails for x cubed at 0 and option 3 fails for x to the fourth at 0, which has f'' = 0 and is nonetheless a strict minimum. The Extreme Value Theorem and the endpoint warning are both exactly as stated in the lesson.
Practise Optimization and Extrema
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