Math 1525 - Spring Semester, 2015 - Course
Policies
Instructor Information:
Deborah Bost Smith
Office: Math Emporium
e-mail: [email protected]
Student Information:
It is very important that you check for any announcements on the
course homepage at least once
Which of the Following is incorrect?
a) The function x) = e" is increasing.
b) The derivative of x) = e"r at x = O is 1.
.3, c) The derivative of fix) = x at x :1 is e.
.3. d) The derivative of x) = x is ex.
w .-. p). The derivative oF for) = xIE at x :1
Given: F(x)=ln Jim #00:?
2.5bz40757452 (VT)
5 . . .
For f(x)=4 I, pack fhe chance Hunt Is closast #0 Fall). a .3 a) PM) = -21;
a) F(o.4)=11.2 b) x): ,7 -
V -. b) f(0.4)=111 c) Fm:
c) f'(0.4)=170 g ,- ) F00=
d) f(0.4)=56.z e) Pinbznhm
Given: for) = InWE
- Correcl
1) If For): %, fhen a value mi in ihe domain of F is:
v ,I a. '3
b. 3
- Correct
2) From fhe Following fable 0? values For +he Funafions, x), got) and my
deiermine which of ne Following srarernents is earrecf up to roundol-F
error.
W
mama-m
m-n
1) Open an Excel window and plot (on the same axes)
the graphs of the Functions Rx) = 3 xi 5
and 90:) = 5x3 + 4x w 293 over the domain [0,10].
Use your graph and table of values to determine
which of the following is a point of intersection
For the two Fu
1) Suppose a company is curreny manufacfung 4'! wa+ches
per day. The variable coal is $210 per wa'l'ch wii'h daily
Fixed cosrs infaling $1464. Whni is the [easr number of
wal'ches Hml need To be produced each day in order 1'0 sell
fhe wal'ches For $234 ea
- Correct
1) The Following fable lisfs fhe population cfw_In thousands) oF
Alaska befvveen ihe years 1920 and 1990.
Populoon If is known fhai a quadroo model
gives a good F to The populafion
mu daro. Firsr. oiign fhe data. Then open
mu an Excel window, ma
1) For 31 years, 1the population of a small town increased From
7042 to 14455 people. Due to a drought, the
population increased by only 289 people over the next 27
years. Which of the Following gives the average rate of
change For the population per year
4) The equal-ion p3 = r2 5 relares cfw_he variables p and r'.
Using his relai'ionship, which of lhe Following is frue ?
a. p is a Function of r and r is also a funcrion of p
b. r is a Function of p . while p is nor a Funcrion of r
c. p is noi- a function
- Correct
1)
Suppose you are baking a cake in an oven at 390'.
Al 2 pm you. fake if on? and puf if on a cooling rack.
If is 76" in The kilchen and offer 20 minutes, fhe cake
has cooled fo 248'. When will flue cake cool fo 104?
CI. 3:00
b_ 3:20
C. 3:10
d_
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Sketching polynomial functions Using the first derivative
Using the second derivative
Using the original function
Example: x^3 6x^2 + 1 First, find the formulas for the first and second derivatives.
Next, analyze the first derivative. Compare your results
?_4.1C:4D?B?3DT
Echo Tech has introduced a new model of fheir camera phone.
The number of sales of fhe phone 9: Weeks aer 1I'l'ie beginning
of The initial sales promotion is given by Six)=150e'5" x." 150,
is x s 20. Find fhe rafe of change of she companys
I II.II-Ill H'HIIIIH- III-n '|.I I I lad-Lu- Illl'u-Ili'u-IIIIII vuluulw II II.II Illullluw 1m, 1- l' III-IlluI-rlu- ulllw- I lulu-nun- u
14432437653131
GWEN the demand function ,0 = 4500121? Determine whether
demand is eiasfic, ineiasfic, or has unif e
The demand funcen For a. pmducf is p = ?5 -~ 3 q where p is
price cfw_in dollars per uni? quantify, q (in cases. The xed
unt. for he product ere $T5, end fhe veriebie reef per unit is $21.
Find ue marginni prot Funcfian and use if at q: 14
+0 esmefe fhe p
14.131433331350'
A manufaci'urer has determined the? :1 employees will produce a foial
of q units oF producf per day where q: (45 mn) :1. IF the demand
funcon is given by p: Emill q, find fhe rare of change of daily
revenue wifh reSpecf to fhe number of e
The demand funcfian For a praducf is p m 60 w 2 5; Where cfw_.2 is
price (in dollars) per unit quanfy, q (in cases). The xed
cash; far fhe produci are $60, and ne variable cfw_:an per mmiir is $20.
Find 4Hue marginai pmf Function and use if ai q:11
fa est
T.4.1b24[544915
There are currently 442 students enrolled in Webster Elementary
School, and the number ot' students is increasing at the rate of
15 students per year. Currently the annual cost to educate one
student is 1,144 dollars, and the cost to educa
A manufaclurer has determined fhal the average Casi per unit
of pradncir when q unifs of the product are produced is given by
nc : 2q+ 3? +10 dollars. If fhe price per unit is p dollars and
fhe number of unirs praduced is if m 400 2p unirs aF produci'
per
IF x) and 90:) are difFarenfinbie Funcfions wifh vaiues
0F the mcfions and fheir derivatives as indicated in 1+1:
fable below, comic fhe derivafive
:5 (Ram) + Mm]
avaiuni'ad af x = 1:
Immmm
.35
. 5?
135
'1'8
.13
1433143319331?
The demand funefian for a product is p : 'F'S - 3 q where p is
price (in dollars) per unit quantify, q (in cases). The xed
005155 For fhe product are $900, and fhe variable :05? per uni? is $10.
Find fhe marginal pmf funei'ian and use if 01
man 24- v
v
dollars Where q is fhe number of gizmus produced per day cfw_15 q s 2(3).
The average cast of a Hakie Gizmo is given by Miq =
Find and inferpref The marginal average cos? when 4 gizmas are
produced per day. Round your answer.
3) Average cost
There are canrenjir #22 laying hens at Egg City Farm. ue fa
surne considerations, ihe number of laying hens is increasing at
he rate of 1'? hens per month. Curreny fhe average number
of eggs per hen is 1143 eggs per manih, and praducan of eggs
is decreasi