題組內容

6. Suppose that f(x) is continuous on [0,6] and f(0) = f(4) = 0. The graph of f'(x) is given as below, but values of f'(1), f"(2) and f'(4) are not determined. It is known that

(c)  Find intervals on which y = f(x) is concave upward. Find intervals on which y = f(x) is concave downward. Find the inflection points of f(x).

詳解 (共 1 筆)

助人為本
助人為本
詳解 #7375184
2026/05/17
我們可以利用一階導數來判斷其凹口向上或向下，如果一邊是向下而另一邊向上(則為反曲點)，同理相反也是
在區間[0,1]，圖形是一條右上的曲線(一階導數向上)，凹口向上
而在區間[1,2]，圖形是由-1到-2，(一階導數向下)，凹口向下
而關鍵在這，x=1處圖形由正變成負，代表其為反曲點
接下來區間[2,4]，圖形從-2一路衝到無窮大，一階導數向上，所以x=2是反曲點
而區間[4,5]，圖形從-無窮大一路衝到x軸(一階導數向上)(凹口向上)
而區間[5,6]，圖形過了最高點後一路往下坡，由上升變下降所以x=5為反曲點
所以可以得到
6a097d1a7bbc9.jpg