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Math 76O-250 Calculus for Business
Self-marking Practice quiz 3

Submit over the internet by 11:59 PM Sunday 15 October 2017
Maximum value toward semester grade is 2 pts
Methods will be discussed in class;
CAUTION: Prof McFarland makes new tests each semester.

Average grade on Spring 2017 paper test # 3 : 7.79 Perfect = 10 See future grade prospects?

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[1]
(a)(1 point) If f(x) = 1
3
x3 - 9x + 2 ,   then find f '(x) by entering integers (like 5, 0, or -2) in the blanks below:
  f '(x) = x3 + x2 + x +
Review rules for derivatives??
 
  (b)(2 pts) Find both CVs (critical values) for f(x) in [1a] above. Then test each CV by entering numbers (not just +/- signs) in the 5 empty boxes of the table below. Scoring: one point for each correct table row
  (c)(2 pts) Using the values of f '(x) you entered in the table below, name the type of CV (max, min, or ledge) in the bottom table row below. Scoring: one point for each correct type of CV.

Note that the
table at the
right is a 1st
derivative test
test value smallest
CV
test value largest
CV
test value
x -4 0 +4
f '(x) 0 0
kind of CV
Relative Max
Relative Min
or Ledge
Max
Min
Ledge
Max
Min
Ledge
Review
these
ideas??
[2]
 
A baseball card store can obtain "Babe Garfield" cards at a cost of $5 per card, and has been selling them at a rate of 50 cards per month for a price of $9. The store is planning to change the card price, and estimates that for each $0.50 per card reduction, 10 more cards will be sold each month. At what price per card will the store owner maximize his/her profit?
  [2a](2 points) For the problem in the box above, choose the best definitions of x and P for translating the words into mathematics. Vague English gets less credit ; thus, "Let x = number of apples John should buy" is better than "Let x = apples". Note : on paper tests, student must write definitions rather than choose among options.
 
Let x = number of baseball cards sold
Let P = price of each baseball card
Let x = baseball cards
Let P = profit
Let x = number of price reductions
Let P = price of baseball cards sold
Let x = price of each baseball card
Let P = profit on all baseball cards sold
Let x = number of baseball cards sold
Let P = profit on all baseball cards sold
Let x = cost of each baseball card
Let P = price of each baseball card
See an example of
this kind of problem ??
  [2b](3 points) Enter integers below (such as 3, 0, or -2), expressing the relationship between the "x" and "P" you defined above. The correct solution to [2b] must use the definitions of x and P from [2a] above, not some other (perhaps unlisted) choice which you might have preferred. If you (incorrectly) thought P = (10 - x)(x + 2), then you would enter "-1", "8", and "20" in the boxes below.
  P(x) = x2 + x +

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