Management Calculus online
Show all analytic work.
a) (5 pts) find the limit of the difference quotient b) (5 pts) find the equation of the tangent line at x= 4, and graph the function f ( x) and
tangent line at x= 4. 2. Using appropriate differentiation techniques (not the limit process), find f '( x ) and
simplify (final results should not have negative exponents) the following: Show all steps
and compute a common LCD.
2
a) (7 pts) f ( x) =
−(2 x + 3 x 2 )3 +
x b) (6 pts) f ( x) = x
2 − 5x c) (7 pts) =
f ( x) ( 3 ( 3x + 1) )[ x 2 + 3] 3. Items cost $6 each to produce and sell for $18 each. The overhead is $1,200.
a) (6 pts) Find the cost, revenue and profit functions. b) (7 pts) Find the (x, y) coordinates of the breakeven point. Also graph the cost and
revenue functions on the same graph and indicate the breakeven point. c) (7 pts) Find the average profit function and the rate of change of the average profit
when x=10 items. 4. The cost
=
C 16 x 2 + 6400 .
(10 pts) Find the (x, y) coordinates of the average cost function when the slope of the
tangent line is horizontal. 5. f ( x) =x3 − 3 x 2 + 4 is the model for a revenue function and x represents years, y=f(x)
represents revenue in thousands of dollars. Assume the model is valid for the years
0≤ x ≤5.
a) (5 pts) Find the rate of change of the revenue in year 3. b) (5 pts) In what years are the rates of change of the revenue equal to zero? c) (5 pts) Graph the revenue function and in what x interval is the revenue decreasing and
in what interval is the revenue increasing? 6. The following data represents a company’s revenue in millions of dollars.
Year:
2003 2005 2007 2008 2010 2011 2012 2013 2016
Revenue:
30
32
34
35 39
39
44
46
50
Let the year 2000 be the base year with x=0.
a) (5 pts) Model the data with a linear function using the points in years 2003 and 2013.
Round computed values to the nearest tenth. Also, using your model predict the revenue
in the year 2017. b) (5 pts) Set up a table of (x, y) values to be used for a least squares model and find a
linear least squares model =
y ax + b for the data. Express the coefficients a and b
accurate to 3 decimal places. Also, what is the R 2 value accurate to 3 decimal places?
Also, using your least squares model predict the revenue in the year 2017. 7. f=
( x)
10 x + 6
a) (3 pts) Using the chain rule, find f ‘(x) and then evaluate f ‘(x) at x=3. b) (4 pts) Graph f(x) over an appropriate domain and graph the tangent line at x=3. c) (8 pts) Find f ‘(x) using the limit of the difference quotient. .

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