Math 148, Summer 2014Number
Final Exam
- The total revenue for selling x units of a product is (9 pts)
a.Compute the average rate of change in on the interval [20, 50]. Be specific and include your units
b.Find the marginal revenue when 50 units are sold and explain what it means in everyday language.
- A product as a daily marginal revenue and a daily marginal cost of If the daily fixed cost is $200, how many units will give maximum profit and what is the maximum profit? (9 pts)
- If the cost, in dollars, of producing x products is . Find the minimum average cost. Use calculus and show your work. (9pts)
- The demand function for a piece of medical equipment sold in a monopoly market is
. Find the elasticity when p = $300. Please conclude whether it is
elastic, inelastic, or unitary elastic. (9 pts)
EXTRA CREDIT: 3 bonus points if there was only one or two minor errors on this page. (3 pts)
- Use the formal definition of the derivative to find if
(6 pts)
- The graph of the function is shown along with the tangent line at the point
/ What is the formula for the slope of the tangent line at the point ?
(2 pts)
- The graph of the function is shown: (8 pts)
/
- State all values of x where
- State all values of x where
- State where
- State where
- For the function shown below, find the following (12 pts)
/ a)
b)
c)
d)
e)
f)At x = 6, is the second derivative positive or negative?
- Write the definite integral that represents the area under the curve shown, and compute the area by hand or with your calculator. (6 pts)
- The annual profit for a store (in thousands of dollars) since 2006 is given by
where x is the number of years past 2006.
Find the inflection point, both the x and y coordinates and explain what the inflection point means in everyday language. (6 pts)
- Find the following: (3 pts each = 24 pts)
a)Find if ,
b)Find
c)Find if
d)Find if
e)Find
f)Find y’ if
g)Find
EXTRA CREDIT: 2 bonus points if only one or two minor errors on this page.(2 pts)