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Unformatted text preview: B us 14B  Online Worksheet #2
Show all work on answer sheet. Then submit as an email attachment or bring to R308d (or R201)
by deadline.
Find all points where the function is discontinuous.
10) 1) Suppose the cost of producing x items is given
by C(x) = 3600  x 3 and the revenue made on the sale of x items is R(x) = 300x  12x 2 . a) Find
the number of items which serves as a
break even point. b) Find quantity to
maximize profit. c) GRAPH/Label CRP Graph this rational function, label the vertical and
horizaontal asymptotes.
5x + 2
2) y =
x+3 Find the average rate of change for the function over the
given interval.
11) y = 6 x 3  2x 2  5 b etween x = 2 and x = 7
Find the derivative. (Section 12.1)
12) y = 17x  2  2x 3  9x 3) A college student invests $7000 in an account
paying 8 % per year compounded annually. In
how many years will the amount at least
quadruple? 13) f(x) = 9x 7/5  5x2 + 104
14) g(x) = 4 x 5 + x4  7x 2 + 3, find g'( 1 ) Find the limit. If possible, factor first.
x 2  100
4) lim
x
10 x  10 5) 6) x x lim lim To find the max or min "x" value, take the first derivative of
the function, set it equal to zero, and solve for "x".
15) If the price charged for a candy bar is p(x) cents,
then x thousand candy bars will be sold in a
x
certain city, where p(x) = 111 . How many
12 x 2 + 7 x  30
x2  9
3
1
1
x+3 3
0 x candy bars must be sold to maximize revenue?
(First, simplify fraction.) 16) A company wishes to manufacture a box with a
volume of 40 cubic feet that is open on top and is
twice as long as it is wide. Find the width of the
box that can be produced using the minimum
amount of material. Find the limit as h approaches zero.
lim (x + h)3  x3
7)
h
0
h 17) S(x) =  x 3 + 6x2 + 288x + 4000, 4 x 20 is an
approximation to the number of salmon
swimming upstream to spawn, where x
represents the water temperature in degrees
Celsius. Find the temperature that produces the
maximum number of salmon. 8) Find the interest earned on $ 10,000 invested for
6 years at 6.9% interest compounded quarterly.
Find all values where the function is discontinuous (the
denominator can never equal zero) and graph (factor first!).
x 5
9) =
2  17x+ 10)
(3 x 18) A piece of molding 155 cm long is to be cut to
form a rectangular picture frame. What
dimensions will enclose the largest area? 1 Answers for Worksheet #2
1. See the pencasts for two
problems similar to this one. Courtesy of Diane – one of your classmates!
13.
f(x) = 9x7/5–5x2+104
f’(x) = x2/510x 7. Revenue is maximized at 5000 units.
Profit is maximized at 4000 units. 14.
g(x) = 4x5+x47x2+3
g’(x) = 20x4+4x314x
g’(1) = 20(1)4+4(1)314(1)
= 204+14 = 30 2. Graph….
Vert asympt: x = 3; Horiz asymp: y = 5
15
Vert Asympt 8. P = $10,000, t = 6, r = 6.9%, m = 4
A = $15,075.26 (TI84 Solver)
Total interest earned:
$15,075.26 – 10,000 = $5,075.26 15. 10
Horiz Asympt 5 To maximize revenue, sell 666,000 candy bars. 0
15 12 9 6 3
5 0 3 6 9 12 3. P = $7,000, r = 8%, m = 1,
A = 4 X $7,000 = $28,000
t
$28000 = $7000(1 + 0.08)
t
4 = 1(1.08)
t=
= 18.01
It takes a little over 18 years to
quadruple, but since interest is only
compounded annually, it will take 19
years to get over 4 times. 4. 5. 6. 16. 9.
Discontinuous at x = 2/3, 5; VA: x = 2/3; HA: y = 0 3 2 4
3
2
1
0
1
1
2
3
4 Surface Area
S’ 0 1 2 3 4 5 6 10. Discontinuous at x = 2, x = 0 (vert
asymptote), x = 2; (also a horiz
asymptote at y = 0) The width of the box to minimize surface area
is 3.11ft. 17.
The temperature to maximize the number of
salmon is 12°C. 11. f(7) = 6(7)3–2(7)25 = 1955
f(2) = 6(2)32(2)25 = 35
ave rate of change = 12.
y = 17x22x39x
y’ = 34x36x29 18. The dimensions to maximize the frame area
are 38.75cm X 38.75cm. ...
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 Spring '08
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