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1) (10 points)

Find the equation of the tangent line to the graph of tex2html_wrap_inline44 at x=3.

2) (30 points)

Compute the following limits:
 
 

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3) (30 points)

Compute the derivative of the following functions. You don't need to simplify your answer:
 
 

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4) (10 points)

The total profit (in dollars) from the sale of x espresso machines is

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Use the marginal profit to approximate the profit from the sale of the tex2html_wrap_inline72 espresso machine.

5) (20 points)

Let tex2html_wrap_inline74 .

a. Find the domain of f(x).

b. Compute f'(x) and find the critical points of f.

NOTE: You may choose to do a single chart for parts c and d.

c. Give the intervals where f is increasing and those where f is decreasing. Find all local maxima and all local minima.

d. Compute f''(x). Give the intervals where f is concave upward and those where f is concave downward. Is there any inflection point for f?

e. If f(x) for tex2html_wrap_inline96 represents the cost function of producing x hundred espresso machines, how many machines would you produce in order to minimize your cost?
 




Lorenzo Sadun

Tue Sep 12 15:10:42 CDT 2000