Prof. A. Suciu Name: depth2pt height-1.6pt width5truecm

MTH 1733 QUIZ 2 Fall 1997

• Sketch the curve $${y=x^3+\frac{3}{2} x^2-6x+4}$$, indicating all relative extreme points and inflection points.

  
  

  
  

• Use derivatives to estimate the value of $${\root{3}\of{27.5}}$$. Compare the answer to the calculator answer--to how many decimals do the two answers agree?

  
  

• For each of the following curves, determine the equations of the asymptotes, if any:
  • $${y=\frac{x-1}{x^2-9}}$$
    
  • $${y=\frac{2x+2}{3x-4}}$$
    
  • $${y=\frac{x^3+2}{x^2+4}}$$
    
  • $${y=\frac{3}{\sqrt{x}}+\frac{x}{2}-5}$$
  
  
• Differentiate the following functions:
  • $${f(x)=(x^3+x^{-\frac{2}{5}})(x^2-x^{\frac{2}{5}})}$$
    
  • $${f(x)=((x^2+1)^3+1)^4}$$
    
  • $${f(x)=\frac{\displaystyle{\frac{1}{x}}-x}{\displaystyle{\frac{1}{x}}+x}}$$