Differentiable?

2013-05-03 2:31 am
Let f(x) = x^(1/3) for x belongs to R. Is the function differentiable at x = 0?
Give your reason.

回答 (4)

2013-05-03 5:45 am
✔ 最佳答案
dx^(1/3) / dx
= (1/3)x^(1/3 - 1)
=x^(-2/3) / 3
-------------------------
For x=0
dy/dx = 0^(-2/3) / 3
=[0^(2/3)]^(-1) / 3
= 0^(-1) / 3
∵ 0^(-1) is undefined.
∴f(x) is not differentiable at x=0.
2013-05-04 2:44 am
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上門補習:
名校中學畢業
學業成績曾試過在全班頭三名之內
教授 DSE 文憑數學 ( 基本課程,M1,M2)
每堂$ 500 (45-60 min)
第一,二堂(試堂) $0 . 免費 (只限兩堂,如試堂不適合可以不上第三堂 )
詢問可電62806183
2013-05-03 6:31 am
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圖片參考:http://imgcld.yimg.com/8/n/HA08446686/o/20130502223014.jpg
2013-05-03 4:23 am
f ' (x) = lim(Δx →0) ( ∛(x + Δx) - ∛x ) / Δx
= lim(Δx →0) ( ( (x + Δx) - x ) / ( ∛(x + Δx)² + ∛((x + Δx)x) + ∛x² ) ) / Δx
= lim(Δx →0) 1 / ( ∛(x + Δx)² + ∛((x + Δx)x) + ∛x² )
= 1 / ( ∛(x + 0)² + ∛((x + 0)x) + ∛x² )
= 1 / (3∛x²)∴ f ' (0) = 1 / (3∛0²) = 1/0 means the function is not differentiable at x = 0.


收錄日期: 2021-04-13 19:27:15
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