math104-s21:hw10
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math104-s21:hw10 [2021/08/25 04:11] pzhou ↷ Page moved from math104:hw10 to math104-2021sp:hw10 |
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| Hint: (1) what are the local min and local max for $2 + \sin(1/x)$? (2) How does multipling the factor $x^4$ change your previous answer? (3) You can try to change the variable, let $u=1/x$, then the function become $(2 + \sin(u)) / u^4$, the question then becomes: "can you find a sequence of local minimums as $u$ goes to $+\infty$?" | Hint: (1) what are the local min and local max for $2 + \sin(1/x)$? (2) How does multipling the factor $x^4$ change your previous answer? (3) You can try to change the variable, let $u=1/x$, then the function become $(2 + \sin(u)) / u^4$, the question then becomes: "can you find a sequence of local minimums as $u$ goes to $+\infty$?" | ||
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| If you find constructing local minimum too difficult, you can prove something weaker: there is a sequence of non-zero critical points of $f$ convergent to $0$, where a critical point of $f$ is a point $x$ with $f' | If you find constructing local minimum too difficult, you can prove something weaker: there is a sequence of non-zero critical points of $f$ convergent to $0$, where a critical point of $f$ is a point $x$ with $f' | ||
math104-s21/hw10.1629864685.txt.gz · Last modified: 2026/02/21 14:44 (external edit)
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