1) (10 points)
Find the equation of the tangent line to the graph of 
at x=3.
2) (30 points)
Compute the following limits:
3) (30 points)
Compute the derivative of the following functions. You don't need to
simplify your answer:
4) (10 points)
The total profit (in dollars) from the sale of x espresso machines is
Use the marginal profit to approximate the profit from the sale of the 
espresso machine.
5) (20 points)
Let 
.
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 
represents the cost function of producing
x hundred espresso machines,
how many machines would you produce in order to minimize your cost?