Math 250 Business Calculus
This is Paper Test # 4 [Go to web quiz 4]

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 25O Test 4 (Hour Exam : perfect=45) given Spring 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 quiz
____________________
Total (max = 45)
Average grade on this test : 31.85
See future grade prospects?

[1](a) (Pg 261, part of #5; this was on previous test, but see [2] below?)(1 pt) Find f '(x) if f(x) = 3x5 - 5x3
 
(Enter numbers in boxes) f '(x) =
 
x4 +
 
x2 +
 
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 all the 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 middle
CV
test value largest
CV
test value
x -2   -½     +2
f '(x)   0   0   0  
kind of CV
Relative Max
Relative Min
or Ledge
Rel. Max
Rel. Min
Ledge
Rel. Max
Rel. Min
Ledge
Rel. Max
Rel. Min
Ledge

 

 
[2] (Pg 261, more of #5; see [1] above?) Let f(x) = 3x5 - 5x3 with domain of f restricted to: 0 x +2
 
(a)(2 pts) Enter ALL 3 CV's for the above f(x) into the 2nd row of the table below. Remember that 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.
 
CV test value CV test value CV
x   1
2
  3
2
 
f (x)          
f '(x)    
kind
of
CV
Rel. Max.
Rel. Min.
Ledge
Rel. Max.
Rel. Min.
Ledge
Rel. Max.
Rel. Min.
Ledge

We did this stuff in class

[3]
(Pg 278 part of #5) A rectangular playground will have an area of 3600 m2 (square meters) meters, and will be enclosed on all sides by a fence.
field
y
x
See a
similar
problem
worked out ?
Write an equation expressing the relationship between the field width "x" and
the length "P" of fence needed to enclose this playground.
[4] (a)(1 pt)(Pg 309 #1f) Use a calculator to express e as a decimal accurate to within 0.01
 
(b)(2 pt)(Pg 326 #25) If 2 = e0.06x, solve for x using natural logarithms, that is, logarithms to the base e [show work]
  (c)(2 pts)(Pg 355 part of #21) If 12 = 4e5k, find the value of Y = 4e10k. Show work. Do not use calculator.
[5]
(a)(2 pts)(part of #21 Pg 288) Find y " if y = -2x3 + 3x2 + 12x - 5 .
Review methods of differentiation ?
(b)(3 pts)(more of #21 Pg 288) For the function y = -2x3 + 3x2 + 12x - 5 , find its one candidate, that is, find the value of x for which y " = 0, and enter this candidate in the table below
[6]
(#15 Pg 228) Test concavity on each side of the candidate in [5] above by filling in the table below.
test value candidate test value
x -2   +2
y"(x)      
Comments Concave up
Concave down
IP
not IP
Concave up
Concave down
[7] (a)(#13,15 Pg 388)(1 pt) Find ( 3 +
2

x3
+ 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 = ' =
v =  ' =
[8] (#3 Pg 403, power changed. Similar problem done yesterday) Find   ( 2x + 6)10 dx
 
"the
thinker"
[9] (#23 Pg 491: similar problem done in class Tuesday) Find  
x

x2
dx