Math 250 Business Calculus
This is Paper Test # 4 [Go to web quiz 4]
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 25O Test 4 (Hour Exam : perfect=45) given Fall 2017
[A] Credit given in proportion to the clarity of your WORK
[B] You need not evaluate anything beyond a point where a calulator is necessary
[C] NON-GRAPHING use of calculators is allowed
__________________
  PRINT name above
grades
 
 
 
  paper test   web work
____________________
Total (max = 45)
Average grade on this test : 27.83
See future grade prospects?

[1](a) (#13 Pg 228 and web quiz 3 ; see [2] below?)(1 pt) Find f '(x) if f(x) = 1
3		 x3 - 9x + 2 :
(Enter numbers in boxes) f '(x) =
 
x2 +
 
x +
 
  ;  
Review methods of differentiation ?
 
(b)(4 pts) Find both CVs (critical values) for f(x) 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 smallest
CV		 test value largest
CV		 test value
x -4   0   5
f '(x)   0   0  
kind of CV
Relative Max
Relative Min
or Ledge		 Rel. Max
Rel. Min
Ledge		 Rel. Max
Rel. Min
Ledge
[2]
(Pg 261 #3, compare with [1] above) Let f(x) = 1
3		 x3 - 9x + 2 with domain of f restricted to: 0 x +2
 
(a)(2 pts) Enter BOTH CV's of f(x) into the 2nd row of the table below. Note: domain endpoints are CV's.
(b)(3 pts) Fill in the remaining empty boxes in the 3rd, 4th, and 5th rows of the table below.
 
Review
these
ideas??
CV test value CV
x   1  
f (x)      
f '(x)  
kind
of
CV		 Rel. Max.
Rel. Min.
Ledge		 Rel. Max.
Rel. Min.
Ledge
You
can
do
this
one
[3]
(#31 Pg 288 one number changed) WalMart can buy American flags at $4 each, and estimates that if they are sold for x dollars per flag (per day), consumers will buy 20 - x flags. At what price should WalMart sell its flags to maximize its (daily) profit P on those flags.
  (2 pts) For the problem in the box above, write an equation showing the relationship between "x" and "P".
 
(Enter numbers in boxes) P(x) =
 
x2 +
 
x +
 
  ;  
Review word problems ?
  (3 points) Differentiate the above P twice, find any CVs of P, and name the x at which P is largest.
 
P '(x) =
 
; P "(x) =
 
. Thus, P is biggest when x =
 
[4] (a)(1 pt)(Pg 309 #1a) Use a calculator to express e2 as a decimal accurate to within 0.01
  (b)(2 pt)(Pg 325 part of #7) Without using a calculator, write e32 as an integer.
  (c)(2 pts)(Pg 309 #21 one number changed) If 23-x = 8x, what is x? (show algebra work)
[5]
(part of #11 Pg 355) Find f '(x) and f "(x) if f(x) = xex
Review methods of differentiation ?
[6]
(more of #13 Pg 228) Find f "(x) if f(x) = 1
3		 x3 - 9x + 2 .
(1 pt) Enter numbers in boxes : f "(x) =
 
x2 +
 
x +
 
  ;  
Review methods of differentiation ?
Find the one candidate of f(x) above by filling in the table below. A candidate is a value of x at which f "(x) is either zero or undefined. ("IP" = "inflection point")
test value candidate test value
x -1   2
f "(x)      
Comments Concave up
Concave down		 IP
not IP		 Concave up
Concave down
[7] (a)(#15 Pg 388)(1 pt) Find ( ex

2		 + x ) dx
Review anti-differentiation methods ?
    (b)(handout)(2 pts) Find


dx    (The integrand is divided by )
    (c)(handout)(2 pts) Find dx
For the remaining 2 problems, if you use substitution, copy the left-hand table (below) into your blue book, and fill in it's 4 empty boxes. If you use integration by parts (IBP), copy the right-hand table (below) into your blue book, and fill in it's 4 empty boxes. Use no isolated differentials, i.e., do not write expressions like "du = 2xdx"
For substitution
u =
du
dx		  =
y(u) =
dy
du		  =
     
For IBP
u = u ' =
v =  v ' =
[8] (#17 Pg 403) Use substitution to find   (x + 1)( x2 + 2x + 5)12 dx
"time to
wake up"
[9] (#3 Pg 490) Use Integration by Parts to find   (1 - x) ex dx