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

(Extrema, Worded Problems)
Numerical answers are in our text, Hoffman 11th 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 2017
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 : 7.79
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grades
 
 
 
  paper test   web quiz
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Total (max = 10)

[1](a) (part of #5 Pg 261)(1 pt) Find y ' if y = 3x5 - 5x3 .
    (Enter numbers in boxes) y ' =
 
x4 +
 
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 9 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 CV test value
x -2   -½   ½   +2
y '(x)              
comments Rel. Max.
Rel. Min.
Ledge
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...
 
(#11 Pg 279 three numbers changed, easier than baseball card problem on web quiz) It costs APPLE COMPUTER $250 to create each i-PAD (in China). APPLE is currently selling each i-PAD for $500, and at that price has been selling 200 i-PADs per month. APPLE plans to change the price, and estimates that for each $1 decrease in price, 5 more i-PADs will be sold each month. At what selling price x will APPLE maximize its profit P on all i-PADs 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 i-PAD" : don't change this definition
 

 
(Helpful step:) Let d = number of $1 price decreases. d =
 
+
 
x
(Helpful step:) Let N = number of i-PADs sold. N =
 
x +
 
 
 
P(x) =
 
x2 +
 
x +
-675 000
  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 ?