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Reviewed CSCA STEM Chinese question · Standard

在微积分中,若函数在某一点的导数大于零,则函数在该点附近通常呈现_的趋势。

  1. 单调递减
  2. 单调递增
  3. 先增后减
  4. 保持不变
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Correct answer

B. 单调递增

Principle or equation

若函数在某点的导数大于零,则函数在该点附近局部单调递增。

Why this answer is correct

导数表示函数的变化率,正导数意味着函数值随自变量增大而增大,因此函数在该点附近呈单调递增趋势。

Example

对于f(x)=x²,在x=1处导数f'(1)=2>0,函数在1附近递增。

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