1. Use implicit differentiation to find the tangent line to the curve  at the point where 








 

2. Let 
1. Find the linearization of  at 






 

2. Use part  to estimate 





3. Suppose a rectangle has a height that is increasing at a rate of 5 cm/sec and a base that is decreasing at a rate of 4 cm/sec. How fast is the area changing when the height is 20 cm and the base is 40 cm? (Half of the credit on this problem will come from an appropriate picture with variables clearly labeled and all values given in the problem clearly stated in mathematical notation.)






 

4. Sketch the graph of a function  that satisfies all of the following:
1. The domain of  is all real numbers except  and 

 
2. has vertical asymptotes of  and 

 
3. and 

 
4. on the intervals  and  and  everywhere else.





5. Let  Then  Find all inflection points of 






 

6. Let 
1. Find all local maximum and minimum values of 






 

2. Find the absolute maximum and minimum value of  on the interval 







7. a.  Find 

 
2. Find 


8. For the graph below estimate each of the following as closely as possible.
1. the intervals on which  is increasing.

 
2. the intervals on which  is concave up, and

 
3. the absolute maximum and minimum values if they exist..
 

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