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Reviewed CSCA STEM Chinese question · Easy

在高等数学中,若函数f(x)在点x₀处可微,则f(x)在x₀处一定。

  1. 连续但不一定可导
  2. 可导但不一定连续
  3. 连续且可导
  4. 既不连续也不可导
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Correct answer

C. 连续且可导

Principle or equation

在一元函数中,可微与可导等价,且可导必连续。

Why this answer is correct

函数在一点可微等价于可导,而可导必连续,因此可微必连续且可导。

Example

例如,f(x)=x²在x=0处可微,且在该点连续。

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