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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PRINT name above
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 +

(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 theseideas??
 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 =