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Reviewed CSCA STEM Chinese question · Standard

在高等数学中,若函数f(x)在点x₀处可导,则f(x)在x₀处一定_。

  1. 连续
  2. 有界
  3. 单调
  4. 可积
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Correct answer

A. 连续

Principle or equation

可导必连续,这是微积分的基本定理。

Why this answer is correct

函数在某点可导,则在该点一定连续;但连续不一定可导。

Example

f(x)=|x|在x=0处连续但不可导,而可导函数如f(x)=x²在x=0处可导且连续。

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