[微積] critical point
有幾題 Calculus 問題,想要請教版上的大大
(1) Consider the function f(x)=xcos(x). Graph y=f(x) on the interval
[-2pi,2pi] and find the equation for all critical points in R and
determined whether they are minimal, maxima, or neither.
想法： 解 f'(x)=0, 可以得到 critical point, 故 cos(x)-xsin(x)=0
tan(x)=1/x, 再來就不知道要怎樣解該方程式的解. 也不知道要怎樣
進一步check 是局部極大 OR 局部極小.
(2) Let's say you start from the base of a mountain at 6 am, and walk up
at any speed so that you arrive at 6 pm. The next day, you take exactly
the same path and descend the mountain, again starting at 6 am and
arriving at the base at 6 pm. Is there necessarily a time of day when
you were at the same point on the mountain, both days?
(Use Intermediate Value Theorem to justify your answer)
想法： 是 上山的畫一條 時間和海拔高度的 curve
下山的再畫一條,然後說兩條 curve 會相交就好了嗎？
那這樣應該沒有用到 intermediate value theorem?
謝謝＠＠
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