Week in Review # 7
MA1'H 142
Sections 5.2,5.3,5.4
Drost-Fall 2014
Oct2A,20L0
decto..s,
,1,
k'-- 2x
1.
t"
[{a1l
l",i
o
2u
(^'*D'
h
rqx; =
(*,n,1 -ij/-,,1
'*"/(v)=
_.2x_
2x
2
x +l
xt+{ =o
--
nr 6)
xt+'l
yl'o 'T,
8z+n(z) - (zxY.>l .-
Find the intervals over which h[x] is decreasing
AND concave up, wnen /r1r.1 =
Q
€"Dq-w)
C&+q)z
L -bfns'
hl- Lt
+z- 4e
a>-i_.'ffi
2X
f++
t+, =.2x,
Lf+$
qd
(rot*
+)"
2x (x" +.{ )= 2* (rz+}
2xP + 8x = 2f + zx
%.
6x =o
x =o
t"s+
tt'e')=
2.
5)"
? *L=-
tJ(t)= 7
2s
Find the critical values for
;i.r .r -l
It.',
lt/t--
a.'
-
.ij
2 -r
>
e+
dorna-r-.t v-+ t "t-t
l
-
fcq = 3::3.
Y-[
I'tv)"
*'u)'
(x-DJv-3-ay+Z
(Y- q-
E{4
J
2.r
.b. r/( r'J - ,! +l
2
(o- D-
-zi-
24 +
4t
(**wY
5'=o
f
2r{=b
t *=24
VL=tz
K=
zf-24
F;q
t ,fA or- I2{7
5.
From the graph below of
3.
a. where is/'[x)
f
> o?
Sketch the graph of a
function/that satisfies
following:
(x),
Domain: All real numbers where x
x-intercepts: (-2,0) and (2,0)
tlr Z) U (2.,0O,1
b. Wliere is/[x) incleasing?
y-intercept: [0,4J
c. Where doesflx] have a relative max
Vertical asymptotes: none
lim
'1y
'[x)
or min?
d. Where does
i
nfl ection
/
tl.re
I -3
g= oo iil" ]'
ftrY)-e 'x+6
f(r.) = "o. lim 0
-+'
.
o
.f
'0 on [-2,0) u [4,*)
/'[x) .0 on (-co,-3),[-3,*2)u {0,4)
f"(x) ,0 on [-oo,-3J u [-3,-1) u {1,6)
'[xJ have a point of
?
x
bl Y(e)v whete 8'+
(,-ttz; u(z rno)
C)
h:he+q-
d) o# tcst
4.
$'=o ' xrr'ta-l
Sketch the graph of a
Jr€{-
^tl-
ilfttt
fnor(
function/that satisfies the
following:
Domain: [-oo,a) u [a,coJ
Vertical asymptotes:x = 4
Horizontalasymptote: y =
-2
x-intercept: [6,0); y-intercept: [0,-3)
l'(x)
4
+++++
^l
-j
I
\t
I
dtc.laas,nl
C-pncoua- d
u
,Yt" :f
. graph below to find
the absolure
exrrema
g?:i::::lil,. varuesJ of f (x)., ;;;;;;,h",.
rntervals below.
a.[-50]
b.[ -
1,
B' SU) = -0.2x + ln[5x
g'(r)'^o,,L 1 -S =o
5>c ?o
5 =-!-
2l
c.[1 , 5]
d.[0
5x'2o'
5
25 = $x-2o
{6 _- 5v
'
, coJ
1tx
3"=o+@
e'[ -m,-1]
(r--Gbs
Mr'rr /.
Gr,va,t, r, -i
cr.br
Ttt
(5v-zo)z
-r-+li { -:l----rl
r.__-J
,
.r
q,t
,
.
G.
ho e(/
&br., rrl t r
r
D
-2.5
u -_(5"-6
/<*
mrro
d' u*ffi,?,,
,'-u,r,
tc,-Lu.q
r,
3"(q) = -
rna4
5
Obs nr,r,
b. ..bs
vot,,j-r
obs ^.il!-1r,1
rr\q^l u, r) velr,rr_ [
4t
norn
;i: ndt
e.;r;:
urrwnen
7. J[x) = xa- 4x3- B0x2-
120 d o ynoir,
9' " q,f - nv:- tboy
S'Cs), +
U
x?-s
,,
6y _2rr) = o
c2
(D= Aof- r8oyl, s4oy-
=Lo"Grf-tx-2I)
It6 e): -{.o(tx* tf,- ztj=- n
5"= lzxz- u4x-tGo
Lll3*a - (ov-4o)
$"{r;=* u.'.
?d1.a,&
X-o) t=9> X=-3
Lf
4r (r-8Xpts);o
X=C, X= 8, X= -5
t"(o)=- n
=9
"'N
.l-€/t
tot(r-9\rt3)=
:o
x3o
x=9
nor, *
rolc. (f_
R,
*(t- lx- 4o) zo
)e
vcLur_s
2;f1'rrn_
on its domain. ljse the
Second' Derivative
-er'vqlrvs Test
when
'|
irappries.
4
- 20]
UC
lrtj* -rnA* at !, -- - 3
= zo(9)G.8 r- 8r - 2\)= + U
")
ry" r,("jlo-?$ tr,:
'1
[,"r*r'----YJ"ft:?
xlcrn,rn
reL muir-l
_:?\o\q
or..u:,grfou" .t
lr,1,,'rr.r
"r"r afte.
N[xJ units of.a product
rlrousand dollars nn
r,lr,,,,'#irl,
,i"naing,
uau".i,riig, when
'
N&)- - ,++ef
/v(xl
-ni*
kg*
=
:f"
d
C,h.o'*ql-
N'* -4x"* 6f-24*+ro
N', =
^
lzt
rcN
'r,z(*'-3y+.)IO
i>4zr
e+qj5 -tz(I:?cI=Di"
2
Yt
'l-' 1)- *hat
is rhe
0",#o7a,k',r,ffr.,,L"r,
1. Apply the graphing strategy to skeiEh rhe
l'1
graphol' ''"-'
ZQe3Xr
Jg}D
-")
.ir- ltl
VA: L=- !S-l+A1 (6 hc
{ ari1t s} ot.r'rn inr ih,trq h ttp\i^,\, x--2
1
=
v3
l-r'
I.r'i.,
/tr.i)c.
.n (t-rz\
2c*
X=-3
u?2
JZ
VA:
+'Vov.-24 = a
IL?'-.t
').1-ltl
- rs
:
6.Il{rl
When ts the rate or L'rrdrr6c ur Lrru pr uuuuL
increasing, and when is it decreasing?
lltt"ll
,r-- |
Ob tultr-t
$cx)= ax*q)Qr-a)
:
b= '[Pt5
fv+i;p<-z)
cktna,qn, Rrx #-z12
hote 6 Sr."loWa* Y,--Z
u t,Lt. asqr41 nz - 2h0.,_5-*l* ar1"', t- 3
trife,rct pts Lo .,--z) ( 4/3$)
12. Find ALL asymptotes for
eacl.r
d.
of the following
1(-l
)c= I
".10*u'
Pbtt{t^r o4^frn g=
0
s-
(ax*{zx-$
13. Let S[f = -6.665t'+0.04t3+1.812+25f represent
the salary you are oflered on your first job after
graduation from A&M, in hundreds of dollars. Over
what intervals is the rate of change of Salary negative?
Define t as the number of years working at this job.
Y = -,oz+7 * . 12 {+ 3.tott25
har. of clta.rgL I Slla,rg
tuhue ,oJr.l rlqfrtt+:
S'/ = -,oGl' t , zl2 ?g,(- --a
no!rle-
Ao Fc5 ---
-5.r'-erx
A.A: =o
3
.1
Ut^f,.Osuxm
6-r''
: x(.1x +zl-x-rf
V.A.: x=o-, y= +L
functions:
').t"2 5.r' ;
/,,.
t')- a.t'l
F(x) =
2x-3
Y--l ) 2{- 5r+tc
?":-2!
- jx+ro
*7x+3
o
""'7tb \
ffq$r<^.
l0 ss.
6X *2./t-f
3co=o
tt-4t-6o:o
^r" 7(t * a) =P
i*
'
X'--(e
t=tio,
l
$tr1I =
l.
(eont-)
3r*
Ytz
9c") = €'r1)€)-(ax-q)O
,f'= .u+a-.ii-;Y
-f
9- .= +
7
on ds d,orna..t,
("*O'
t*t)'
-=
S'= ..t*
"4'
\r E
9''= - zo1.*)l(; = '20
@'
-tlsrt
J
I
i
-
-3'
t^
o
6n
3
14. Find the limit of each of the following:
-.
-8x+12
a, ;:;
lrm3xt
,4x3 -100x =C)
b.
lim
c.
lim
-)
6x-
-4x+)
nx' + x1
6x3
0
z
-4xt +5
xr +lx+t
-
=
=4
e.
l:g.
(s
-ae^) = $
r?O
fu^\,
|
=o
x-7 rc
x-> -/x
f =o