y=(x^2+x+1)/x

Frequently Asked Questions

• Evaluate the derivative of \(y=(x^2+x+1)/x\)

  

  $$y^{\prime }=\frac{x^2-1}{x^2}$$

• Find the domain of \(y=(x^2+x+1)/x\)

  

  $$x\ne 0$$

• $$\text{Find the }x\text{-intercept/zero}$$ of \(y=(x^2+x+1)/x\)

  

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

• Find the y-intercept of \(y=(x^2+x+1)/x\)

  

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

• Find the critical numbers of \(y=(x^2+x+1)/x\)

  

  $$\begin{array}{rl}& x=1\\ & x=-1\end{array}$$

• Find the local extrema of \(y=(x^2+x+1)/x\)

  

  $$\begin{array}{rl}& \text{The local minimum is}3\text{at}x=1\\ & \text{The local maximum is}-1\text{at}x=-1\end{array}$$

• Find the increasing or decreasing interval of \(y=(x^2+x+1)/x\)

  

  $$\begin{array}{rl}& \text{The increasing interval is}x\in \left(-\infty ,-1\right]\cup \left[1,+\infty \right)\\ & \text{The decreasing interval is}x\in \left[-1,0\right)\cup \left(0,1\right]\end{array}$$

• Find the range of \(y=(x^2+x+1)/x\)

  

  $$y\in \left(-\infty ,-1\right]\cup \left[3,+\infty \right)$$

• Find the vertical asymptotes of \(y=(x^2+x+1)/x\)

  

  $$\begin{array}{rl}& x=0\end{array}$$

• Find the horizontal asymptotes of \(y=(x^2+x+1)/x\)

  

  $$\text{No horizontal asymptotes}$$

• Find the oblique asymptotes of \(y=(x^2+x+1)/x\)

  

  $$y=x+1$$

• Determine if even, odd or neither of \(y=(x^2+x+1)/x\)

  

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

• Find the stationary points of \(y=(x^2+x+1)/x\)

  

  $$\left(-1,-1\right),\left(1,3\right)$$

• Find the inflection points of \(y=(x^2+x+1)/x\)

  

  $$\text{No inflection points}$$

• Testing for symmetry about the origin of \(y=(x^2+x+1)/x\)

  

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

• Testing for symmetry about the x-axis of \(y=(x^2+x+1)/x\)

  

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

• Testing for symmetry about the y-axis of \(y=(x^2+x+1)/x\)

  

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

• $$\text{Solve for }x$$ of \(y=(x^2+x+1)/x\)

  

  $$\begin{array}{rl}& x=\frac{\sqrt{-3-2y+y^2}-1+y}{2}\\ & x=\frac{-\sqrt{-3-2y+y^2}-1+y}{2}\end{array}$$

• $$\text{Solve for }y$$ of \(y=(x^2+x+1)/x\)

  

  $$y=\frac{x^2+x+1}{x}$$

• Rewrite in polar form of \(y=(x^2+x+1)/x\)

  

  $$\begin{array}{rl}& r=\frac{\cos \left(\theta \right)+\sqrt{-3{\cos }^2\left(\theta \right)+2\sin \left(2\theta \right)}}{\sin \left(2\theta \right)-2{\cos }^2\left(\theta \right)}\\ & r=\frac{\cos \left(\theta \right)-\sqrt{-3{\cos }^2\left(\theta \right)+2\sin \left(2\theta \right)}}{\sin \left(2\theta \right)-2{\cos }^2\left(\theta \right)}\end{array}$$