Math 250 Business Calculus
This is Paper Test # 3 [Go to web quiz 3]

(Extrema, Worded Problems)
Numerical answers are in our text, Hoffman 8th edition;
Methods will be discussed using other problems
Links to other web pages were not on original test;
CAUTION: Prof McFarland makes new tests each semester.

Mathematics 250 Test 3 Quiz (Perfect = 10) given Spring 2009
Credit given in proportion to the clarity of your WORK
You need not evaluate anything beyond a point where a calulator is necessary
Average grade on this test : 7.75
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Total (max = 10)

[1](a) (#15 Pg 212)(1 pt) Find y ' if y = x4 - 4x3 + 10 .
(Enter numbers in boxes) y ' =
 
x3 +
 
x2 +
 
x +
 
 
Review methods of differentiation ?
 
 
 
(b)(4 pts) Find both CVs (critical values) for y in [1a] above. Then test each CV by filling in the 7 empty boxes of the table (right).
Note that the table at the right is a   1st derivative test
Review these
ideas??
test value CV test value CV test value
x -2   2   5
y '(x)          
comments Rel. Max.
Rel. Min.
Ledge
Rel. Max.
Rel. Min.
Ledge

[2]  
Once upon a time, there was a
wicked Math Prof who loved to
write word problems...
 
(#5 Pg 260 underlined number changed) COMPUTER WORLD is currently selling the DVD-copier X-COPY for $40 per box, and at that price has been selling 50 boxes per month. The store plans to change the price, and estimates that for each $1 increase in price,  5  fewer boxes will be sold each month. If the manufacturer charges COMPUTER WORLD $25 for each box of X-COPY, at what selling price x will COMPUTER WORLD maximize its profit P on all boxes of X-COPY sold?
  (3 points) For the problem in the box above, complete the equation which expresses the relationship between x and P (show work: one number given as a reality check).
[Note : x = "selling price of one box of X-COPY " :
you must not change this definition of x
]
 
P(x) =
 
x2 +
 
x +
-6250
  In the space below, differentiate the above P twice and find any CVs of P (for one point). Finally (for one more point) name the value of x at which P is largest.
 
 
P '(x) =
 
 
P "(x) =
 
 
Thus, P is biggest when x =
 
 
See a similar worded problem translated ?