EXERCISE 1:

Given the following function: = +

a) Findtheextremepoints,andprovewhichonesofthemareMAXIMAandMINIMA(15points)

b) Find the inflection points (5 points)

c) Draw the graph of the function (5 points)

EXERCISE 2: Suppose that the revenues function of a certain product in function of the thousands of units sold yearly (x) is: R(x) = -x2 +10x -3 And the function of costs is: C(x) = x3 - 3x2 -x +12

a) Whatisthefunctionofprofits?(5points)

b) Is there a sales level that maximizes profit? If so, what are the points of maximum profit? (5 points)

c) What should be the sales that give the largest yearly revenue? (5 points)

d) What should be the sales that give the minimum yearly cost? (5 points)

e) WhatisthefunctionofMarginalCost?WhatistheMarginalCostwhenx=3?(5points)

EXERCISE 3: Draw and find the area surrounded by the graph generated by:

-Thefunction()=3 +22 +65, - The X-axis, and - The points X=1 and X=3