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Math 76O250 Calculus for Business
Selfmarking Practice quiz 4
(Relative Extrema , Antiderivatives)
Submit over the internet by 11:59 PM Sunday 28 October 2017
Maximum value toward semester grade is 4 pts
Methods will be discussed in class;
CAUTION: Prof McFarland makes new tests each semester.
Average grade on Fall 2017 paper test #4 : 27.83  perfect = 45  See future grade prospects? 
[1]  (a)(1 pt) Find f '(x) if f(x) = x^{3}  3x^{2}  9x + 1 .  
f '(x) = x^{3} + x^{2} + x +  


(b)(4 pts) Find both CVs (critical values) for f(x) in [1a]
above. Then test each CV by entering numbers in the
12 empty boxes of the table below. Scoring: 1 point for each CV (top two answer boxes) ; 1 point for each of the remaining 2 rows below 


[2] 


(a)(1 pt) Enter BOTH CV's for the above f(x) into the 2nd row of the table below, as well as a test value between.  
(b)(4 pts) Fill in the remaining empty boxes in the 3^{rd}, 4^{th}, and
5^{th} rows of the table below. Thus, you will display both a graph test and a 1^{st} derivative test for these two CV's. Scoring : 1 point for each answer in bottom row ; ½ point each for other table entries 


[3] 



(a)(2 points) For the problem enclosed above, let "x" be the edge length of cutout squares, as shown, and let V be the volume of the resulting box. Enter integers below (such as 3, 0, or 2), expressing the relationship between "x" and "V". Thus, if you (incorrectly) thought V = (10  x)(x + 2), then you would multiply out the product and enter "0", "1", "19", and "20" in the boxes below.  
V (x) = x^{3} + x^{2} + x + 
(b)(3 points) Put aside (for the moment) any physical restrictions on x, and find the two values of x at which V ' = 0 ; you will need the quadratic formula to find these numbers. Enter them as CVs in the table below, and complete the 2nd derivative test below, thus answering the question in the problem above. Scoring : ½ point for each of 6 correct table boxes below  


As to those "physical restrictions" : cut yourself a 6" by 8" rectangle and use the larger CV above to build a box ; what happens? (unscored) 
[4]  (a)(3 pts) If q represents the number of lamps sold, and if p represents the price of each lamp, and if p and q are related by the equation : q = 60  0.1p , then calculate the elasticity of demand when p = 200. [See sample problem] 
elasticity of demand =  
(b)(2 pts)) The gross national (GNP) product of Singapore was $100 billion in 2000, and $200 billion in 2010. If Singapore's GNP is growing exponentially over time, what should it be in 2020? [See sample problem]  
Singapore's GNP = $ billion 
[5] 


AFTER finding these derivatives, let "x" = 1, to simplify your entries below.  
(a)(3 pts) f '(1) =  
(b)(2 pts) f "(1) =  

[6] 


Scoring : 1 point for each table box below  


See a similar but somewhat harder problem in assignment #7 







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