f(x)=xlog (x)

Frequently Asked Questions

• 求导数 \(f(x)=x\log \left(x\right)\)

  

  $$f^{\prime }\left(x\right)=\frac{\ln \left(x\right)+1}{\ln \left(10\right)}$$

• 查找域 \(f(x)=x\log \left(x\right)\)

  

  $$x>0$$

• $$\text{找到 }x\text{ 截距/零}$$ \(f(x)=x\log \left(x\right)\)

  

  $$x=1$$

• 找到 y 轴截距 \(f(x)=x\log \left(x\right)\)

  

  $$\text{No y-intercept}$$

• 找到临界点 \(f(x)=x\log \left(x\right)\)

  

  $$x=\frac{1}{e}$$

• 找到局部极值 \(f(x)=x\log \left(x\right)\)

  

  $$\begin{array}{rl}& \text{The local minimum is}-\frac{{\log }_{10}\left(e\right)}{e}\text{at}x=\frac{1}{e}\end{array}$$

• 查找递增或递减区间 \(f(x)=x\log \left(x\right)\)

  

  $$\begin{array}{rl}& \text{The increasing interval is}x\ge \frac{1}{e}\\ & \text{The decreasing interval is}0<x\le \frac{1}{e}\end{array}$$

• 查找范围 \(f(x)=x\log \left(x\right)\)

  

  $$f\left(x\right)\ge -\frac{{\log }_{10}\left(e\right)}{e}$$

• 找到垂直渐近线 \(f(x)=x\log \left(x\right)\)

  

  $$\text{No vertical asymptotes}$$

• 找到水平渐近线 \(f(x)=x\log \left(x\right)\)

  

  $$\text{No horizontal asymptotes}$$

• 找到斜渐近线 \(f(x)=x\log \left(x\right)\)

  

  $$\text{No oblique asymptotes}$$

• 确定是偶数、奇数还是两者都不是 \(f(x)=x\log \left(x\right)\)

  

  $$\text{Neither even nor odd}$$

• 求驻点 \(f(x)=x\log \left(x\right)\)

  

  $$\left(\frac{1}{e},-\frac{{\log }_{10}\left(e\right)}{e}\right)$$

• 找到拐点 \(f(x)=x\log \left(x\right)\)

  

  $$\text{No inflection points}$$

• 测试关于原点的对称性 \(f(x)=x\log \left(x\right)\)

  

  $$\text{Not symmetry with respect to the origin}$$

• 测试关于 x 轴的对称性 \(f(x)=x\log \left(x\right)\)

  

  $$\text{Not symmetry with respect to the x-axis}$$

• 测试关于 y 轴的对称性 \(f(x)=x\log \left(x\right)\)

  

  $$\text{Not symmetry with respect to the y-axis}$$