Math 250 Business Calculus
This is Paper Test # 2 [Go to web quiz 2]

Numerical answers are in our text, Hoffman 11th ed.;
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.
Math 25O Test 2 (Hour Exam : perfect = 45) 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
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grades
 
 
 
  paper test   web quiz
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Total (max = 45)
Average grade on this test : 31.57
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[1] (Handout #1: n,d,p,k,j)(1 pt each) If f(x) = 3x + 2 and g(x) = x2 - 1, enter integers (such as 7, 1, 0, or -4) to find:
  (a)   g( -1 )   =  
 
Cathy won't speak to
me unless I solve
these problems
(b) f(x + 1)   =
 
x +
 
(c)   g(x - 1) =
 
x2 +
 
x +
 
(d)   f(g(x))   =
 
x2 +
 
x +
 
(e) f(f(x)) =
 
x +
 
[2] (a)(Pg 42 #49)(3 points) Students at UW-Janesville may either pre-register on the web before 17 January 2006, or register in person after 8 A.M. on that date. The registrar handles 35 students per hour in person, and by noon of 17 January 2006, a total of 360 students had been registered, including those who pre-registered before 17 January 2006. Let N be the total number of students registered as of x hours after 8 A M. on 17 January 2006. :
N =
 
x +
 
  (enter numbers in boxes)
(b)(Pg 26 #31)(2 pts) Find the two points at which the graphs of [ y = x2 ] and [ y = 3x - 2 ] intersect. Display algebra work as you solve this problem. Check by substitution or graphing calculator output do NOT count as algebra
graph not to scale

[3]
(Pg 62 #59) An open box with a square base is to be built for exactly $48. The sides of the box cost $3 per square meter, and the base costs $4 per square meter. Express the Volume V of the box in terms of the length x of one side of its base (see figure).
x
Review a similar problem?
V =
 
x3 +
 
x2 +
 
x +
 
[4]
(a)(Pg 75 #19)(3 pts) Find the limit or claim the limit does not exist :
x 5
   x2 - 3x - 10

x - 5
.
 
(b)(Pg 130 #61a)(2 pts) The population of Wales x months from now is P = 2x + 4x + 5000  
At what rate will the population of Wales be changing nine months from now ? (Answer is less than 100)
Method (not given on test): Rates are derivatives. Find P' and evaluate at x=9

[5] (Pg 186 part of #1) Use the LIMIT METHOD to find f '(x) if f(x) = x2 - 3x + 1.
The answer is that f '(x) = 2x - 3, but DO NOT USE "QUICKIE" RULES (such as the power rule) to find f '(x). Also, you must correctly use limit notation at least twice for full credit (see problem [4] above as an example). This is the only exam problem requiring the limit method to find f '(x).

[6]
(Handout, and Pg 128 #21) For this question , DO NOT use the limit method, or the product rule, or quotient rule. No credit if you use any of these 3 methods.
(a)(1 pt) Find f '(x) if f(x) =  1
x
 +   1 
x2
 - 
"These are cute (like me),
but be careful:
they have teeth
(like me)
(b)(2 pts) Find f '(x) if f(x) = 
(c)(2 pts) Find f '(x) if f(x) = 
For the remaining problems on this test, you may use any rule or method for full credit, including the product and quotient rules. The limit method should be avoided because it would be very difficult to use properly. Showing your methods clearly may save you points.
[7] (Pg 156 #35 exponents changed, difficulty the same) Find f '( x) if   f(x) = (x + 2)9(2x - 1)8
Practice choosing the correct methods ?

[8] (Pg 181 #11) Use implicit differentiation to find y' (the first derivative of y)
if   x3 + y3 = xy . Thus, do NOT first solve for y (it would be hard), but rather : differentiate both sides of the given equation. Your answer to [8] must be an equation with y ' alone on the left side ;
the right side of your answer will contain the variables x and y, but must not contain y' .

[9] (Pg 143 #43 one number changed) Find y', y", and y''' if y = 2x5 - 4x3 + 9x2 - 6x - 2.