1) y = – x3 + 8×2 – 5x + 3
a) Graph “y”. Be sure to label all maximum and minimum points and
b) Graph the slope of “y” directly below “y”. Line up the graphs so that the “x”
values of the two graphs coincide.
Professor Rones page 2
2) y = ( 2×3 – 8x)4
Find dy/dx when X = – 72
3) A monopolist sells a product in two separate markets at different prices; i.e., he price
discriminates. The demand curves in these markets are:
PA= 100 – QA and Pg = 60 – 0.5 QB His average cost function (ATC) is: ATC = Q + 100/Q where Q = QA + QB
In your calculations, let it be defined as profit.
(Hint: Find an equation for it. Then replace with QA+ Qe. Then, maximize with respect to QA and QB.)
a) Use Cramer’s Rule to find the profit maximizing quantities QA* and Q8*.
(If you absolutely do not remember Cramer’s rule, do it any way you can.)
You do NOT have to check second derivative conditions for a maximum.
b) Find the maximum profit, T*
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