f(x)=x^3-2x^2-25x+50

Frequently Asked Questions

• 求导数 \(f(x)=x^3-2x^2-25x+50\)

  

  $$f^{\prime }\left(x\right)=3x^2-4x-25$$

• 查找域 \(f(x)=x^3-2x^2-25x+50\)

  

  $$x\in \mathbb{R}$$

• $$\text{找到 }x\text{ 截距/零}$$ \(f(x)=x^3-2x^2-25x+50\)

  

  $$x_1=-5,x_2=2,x_3=5$$

• 找到 y 轴截距 \(f(x)=x^3-2x^2-25x+50\)

  

  $$f\left(0\right)=50$$

• 找到临界点 \(f(x)=x^3-2x^2-25x+50\)

  

  $$\begin{array}{rl}& x=\frac{2+\sqrt{79}}{3}\\ & x=\frac{2-\sqrt{79}}{3}\end{array}$$

• 找到局部极值 \(f(x)=x^3-2x^2-25x+50\)

  

  $$\begin{array}{rl}& \text{The local minimum is}\frac{884-158\sqrt{79}}{27}\text{at}x=\frac{2+\sqrt{79}}{3}\\ & \text{The local maximum is}\frac{884+158\sqrt{79}}{27}\text{at}x=\frac{2-\sqrt{79}}{3}\end{array}$$

• 查找递增或递减区间 \(f(x)=x^3-2x^2-25x+50\)

  

  $$\begin{array}{rl}& \text{The increasing interval is}x\in \left(-\infty ,\frac{2-\sqrt{79}}{3}\right]\cup \left[\frac{2+\sqrt{79}}{3},+\infty \right)\\ & \text{The decreasing interval is}\frac{2-\sqrt{79}}{3}\le x\le \frac{2+\sqrt{79}}{3}\end{array}$$

• 查找范围 \(f(x)=x^3-2x^2-25x+50\)

  

  $$f\left(x\right)\in \mathbb{R}$$

• 找到垂直渐近线 \(f(x)=x^3-2x^2-25x+50\)

  

  $$\text{No vertical asymptotes}$$

• 找到水平渐近线 \(f(x)=x^3-2x^2-25x+50\)

  

  $$\text{No horizontal asymptotes}$$

• 找到斜渐近线 \(f(x)=x^3-2x^2-25x+50\)

  

  $$\text{No oblique asymptotes}$$

• 确定是偶数、奇数还是两者都不是 \(f(x)=x^3-2x^2-25x+50\)

  

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

• 求驻点 \(f(x)=x^3-2x^2-25x+50\)

  

  $$\left(\frac{2-\sqrt{79}}{3},\frac{884+158\sqrt{79}}{27}\right),\left(\frac{2+\sqrt{79}}{3},\frac{884-158\sqrt{79}}{27}\right)$$

• 找到拐点 \(f(x)=x^3-2x^2-25x+50\)

  

  $$\begin{array}{rl}& \left(\frac{2}{3},\frac{884}{27}\right)\end{array}$$

• 测试关于原点的对称性 \(f(x)=x^3-2x^2-25x+50\)

  

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

• 测试关于 x 轴的对称性 \(f(x)=x^3-2x^2-25x+50\)

  

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

• 测试关于 y 轴的对称性 \(f(x)=x^3-2x^2-25x+50\)

  

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